The Foreign Secretary said the Russian leader is a 'desperate rogue operator' who should not be rewarded for his aggression.
Government officials are concerned Putin could launch attacks on Moldova or Georgia if he is allowed to keep hold of Ukrainian territory, dragging the conflict on for years to come.
In a major foreign policy speech last night, Miss Truss warned if he 'succeeds there will be untold further misery across Europe and terrible consequences across the globe'.
She said Britain and its allies must 'keep going further and faster to push Russia out of the whole of Ukraine'.
And in an indication that the battle over Ukraine could drag on, she argued 'we must be prepared for the long haul'.
The shocking prediction came as the human cost of war was underlined by a heartbreaking triple funeral in Ukraine which showed the true human cost of the savagery that Russia's leader has unleashed on his neighbour.
Yuri Glodan was wrecked with the pain of loss and disbelief when he was forced to bury his beloved three-month-old daughter Kira, his wife Valeria and his mother-in-law Lyudmila after they were killed in a Russian rocket strike on their apartment building on Saturday.
It is understood ministers are concerned Putin could resort to using short range nuclear missiles or chemical weapons as he becomes increasingly desperate.
Miss Truss is firmly making the case behind closed doors that Russia should not be given any Ukrainian territory in any peace talks.
She argued the crisis in Ukraine must be the catalyst for an overhaul to the West's approach to international security.
In his latest chilling threat to the West, Putin vowed to use nuclear weapons against any country that dares to 'interfere' with Russia's war in Ukraine.
The despot, addressing legislators in St Petersburg, said his response to anyone who 'threatens' Russia will be 'lightning-fast' and deadly.
'If someone intends to interfere in what is going on from the outside they must know that constitutes an unacceptable strategic threat to Russia. They must know that our response to counter strikes will be lightning fast. Fast,' he said.
'We have all the weapons we need for this. No one else can brag about these weapons, and we won't brag about them. But we will use them.'
Though Putin did not mention nuclear weapons directly, he was almost certainly referring to Russia's new Sarmat 2 nuclear missile which was tested for the first time just days ago and that he boasted is unlike any other weapon in the world.
The dire threats came as Moscow claimed to have carried out a missile strike in southern Ukraine to destroy a 'large batch' of Western-supplied weapons.
Miss Truss said the UK needed to strengthen its military while building alliances with free nations around the world, using their economic power to deter aggressors who 'do not play by the rules'.
She said the G7 group of leading industrialised nations should act as an 'economic Nato' defending collective prosperity, while the Western military alliance must be prepared to open its doors to countries such as Finland and Sweden.
Speaking at the Mansion House in the City of London, Miss Truss singled out China, which has refused to condemn the invasion of Ukraine, while increasing imports from Russia and commenting on 'who should or shouldn't be a Nato member'.
'China is not impervious. They will not continue to rise if they do not play by the rules,' she said.
'China needs trade with the G7. We represent around half of the global economy. And we have choices.
'We have shown with Russia the kind of choices that we're prepared to make when international rules are violated.' Miss Truss said the international architecture intended to guarantee peace and prosperity had failed Ukraine in the face of an attack by a 'desperate rogue operator', in the shape of Putin, with no interest in international norms.
'Russia is able to block any effective action in the UN Security Council. Putin sees his veto as a green light to barbarism,' she said.
In the short term, she said Western allies must 'double down' on support for the government in Kyiv, providing the heavy weaponry it needs 'to push Russia out of the whole of Ukraine'.
At the same time, she said the events of the past months must be 'a catalyst for wider change'.
'Now we need a new approach, one that melds hard security and economic security, one that builds stronger global alliances and where free nations are more assertive and self-confident, one that recognises geopolitics is back,' she said.
At home, she said that should mean an increase in defence spending with the Nato minimum of two per cent of national income a 'floor not a ceiling'.
The European Union warned Russia on Wednesday it would not bend to 'blackmail' over its support for Kyiv, after the Kremlin cut off gas supplies to Bulgaria and Poland.
As the war, which has already claimed thousands of lives, entered its third month, Kyiv conceded that Russian forces had made gains in the east.
Russia's military offensive saw it capture a string of villages in the Donbas region, now the immediate target of its invasion force.
And in its economic standoff with the West, Moscow cut off gas supplies to Bulgaria and Poland, two EU and NATO members backing Ukraine in the conflict.
However later Wednesday in Brussels, Ursula von der Leyen, the president of the European Commission, said Poland and Bulgaria are now receiving gas from their EU neighbours.
She described the announcement by Russia's state energy giant Gazprom as 'another provocation from the Kremlin' that would be countered.
'It comes as no surprise that the Kremlin uses fossil fuels to try to blackmail us... Our response will be immediate, united and coordinated.
'Both Poland and Bulgaria are now receiving gas from their EU neighbours,' she said. 'The era of Russian fossil fuels in Europe will come to an end.'
EU officials said energy ministers from across the bloc will meet on Monday to discuss the situation.
European powers have imposed massive sanctions on Russia since Putin's decision to invade his neighbour, while shipping weapons to Ukraine's defenders.
But they have moved slowly on hitting Moscow's vast gas exports, with many EU members - notably industrial giant Germany - reliant on Russian energy to keep their lights on.
Putin has attempted to turn up the pressure by insisting that Russia will only accept payments for gas in rubles - hoping to force his foes to prop up his currency.
Gazprom announced the halt of gas to both Poland and highly dependent Bulgaria, saying it had not received payment in rubles from the two EU members.
But von der Leyen said that 'about 97 percent' of all EU contracts explicitly stipulate payments in euros or dollars - and warned importing firms off paying in rubles.
'This would be a breach of the sanctions,' she told reporters.
The European Commission on Wednesday sought to lend Kyiv economic support by proposing a suspension of import duties on Ukrainian goods, but the idea still needs to be approved in a vote by the bloc's 27 members.
The moment he had to bid his final farewell – before the three coffins were borne away by pall bearers to the newly dug grave – was when Yuri Glodan at last gave himself up to an all-consuming grief.
His face racked with the pain of loss and of disbelief that on this sunny spring morning such a nightmare should be unfolding, he flung himself on each casket sobbing.
First that of his mother-in-law Lyudmila, then his wife Valeria’s – and finally the tiny, amber casket containing Kira, his beloved three-month-old daughter, with the smiling blue eyes she’d inherited from her mother.
Clutching one of her favourite soft toys, Yuri asked over and over why this had to happen to them, to his precious little family killed when two Russian cruise missiles had slammed into the third and fourth floors of their apartment block at 2.30pm last Saturday afternoon.
Eight people died in what has been described as Putin’s Easter massacre.
It had been such a happy day as Yuri, Valeria and Lyudmila prepared to mark Kira’s first Orthodox Christian Easter Sunday, a reason to celebrate amid the gruelling misery of these past weeks of war.
A chef and talented baker, Yuri had been working 13-hour shifts making Easter cakes for others. Now it was time for his own loved ones. He’d just slipped out to the supermarket for more provisions when the missiles struck. At that instant, everything was taken from him and three generations of a family were obliterated.
The funeral yesterday was always going to be an ordeal, but the 30-yea-old had displayed incredible composure and dignity throughout the hour-long service at the magnificent Transfiguration Cathedral on Odesa’s central Soborna Square.
Despite the harsh wail of air raid sirens earlier, Odesa had gathered to pay its respects, the crowd watching in sombre silence as at 11am, two white hearses arrived. The only sound was birdsong – and the constant whirr of cameras from the assembled media.
Sixteen men, dressed in black, approached the hearses and opened the doors.
Three of them lined up facing the cathedral, holding before them Yuri’s favourite photographs of the women he loved. Another three carried wooden crosses etched with the names, birth dates – and that fatal day of April 23, 2022 when he lost them.
Then the coffins: four pall bearers each for Valeria and her mother – but just two for the little Kira. Ashen-faced, the pall bearers struggled to contain their emotions as they moved towards the ornate main doors of the cathedral. Behind them came Yuri, dressed in a navy-blue suit and tie, accompanied by his mother Nina, sister Anastasia, and his father, also Yuri.
Inside, were around 100 mourners – family, friends, and neighbours – many of them distressed. One young woman wept uncontrollably throughout the service. Orthodox tradition is that the coffins of the dead usually remain open.
But the injuries to Lyudmila, Valeria and Kira made this impossible. Yuri held his mother’s hand as the mourners lined up to offer their condolences and place flowers in a steel basket next to the coffins. He described Valeria as ‘perfect. She was a gift from God’.
The outpouring of sympathy and love must help, but one wonders what comfort mere words can provide given the scale of Yuri’s loss.
He and Valeria were only starting out, Kira the first child of the family they planned to build together.
As the opening prayers began Anastasia, Yuri’s 21-year-old sister, tried to stem the tears streaming down her cheeks.
‘We are honouring the memory of a mother and daughter who tried to protect their child,’ Alexander Malichenko, the cathedral’s archpriest said. ‘We always need to remember that God is above us. He will punish those who committed these crimes.
‘These people, especially this child...’ he says, gesturing to Kira’s tiny coffin, ‘…they will be forever in heaven as heroes.’ Yuri’s gaze never left the coffins throughout the service which concluded with mourners lining up to cover them in red carnations.
Then, as the congregation poured back out on to Soborna Square, with Yuri calmly walking behind the caskets, two explosions echoed from faraway, a reminder that, even if they pray to God, Ukrainians are never far away from the threat of war.
For the short, final journey to the cemetery Yuri Glodan travelled in the hearse carrying his wife and daughter, perhaps lost in memories of happier times.
He had fallen head over heels for the former journalism student when they met at a party in 2013. Friends say he loved her infectious laugh, her positive outlook, and trademark bright floral dresses. The shared a passion for travel, photography, good food and fine wines and had a joyful wedding in August 2019. Just one week before her death, Yuri hosted a barbecue at their home to mark his wife’s 28th birthday. She celebrated with her two best friends, Alyona Syritka and Ilyashenko.
Now, the young women were standing in front of her grave.
The eulogies they had written were read out by one of the funeral directors. Alexandra described a beautiful soul who had been ‘stolen away’ from her.
Alyona wrote of ‘dear Lera’ who discovered ‘the secret of life’ after the birth of her baby girl, of how Valeria and Lyudmila ‘were beside themselves with happiness when the little angel Kira appeared’.And then the flower strewn coffins of grandmother, mother and baby were lowered into the ground.
Just one tragedy, among tens of thousands of stories of heartbreak and loss in Ukraine since Russia’s invasion began, but the brutal end to Kira’s short life has touched millions across the world.