The Russian president said he had placed Moscow's nuclear forces on a "special regime of combat duty" in response to "aggressive statements" from members of the Nato defence alliance.
Kremlin spokesman Dmitry Peskov said the comments which forced the Russian president's hand were "absolutely unacceptable" but resisted naming the person who was to blame.
"I would not call the authors of these statements by name, although it was the British foreign minister," he said.
It was unclear which of Ms Truss's comments the Kremlin was referring to, but Mr Peskov said "statements were made by various representatives at various levels on possible altercations or even collisions and clashes between Nato and Russia".
The government has dismissed Russia's criticism of Ms Truss, ITV News Correspondent Daniel Hewitt reports
Chancellor Rishi Sunak described the claim as "rubbish" and said the Foreign Secretary was doing a "brilliant job" in helping get support for sanctions against "the Putin regime".
Scotland’s First Minister Nicola Sturgeon said: “Whatever political disagreements any of us have with Liz Truss – and I have many deep differences with her – we should not fall for this transparent Russian attempt to divert.
“The only person responsible for Putin’s despicable nuclear threat is Putin.”
An ally of Ms Truss hit back at the Kremlin, saying "nothing Liz has said warrants that sort of escalation. It's clearly designed to distract from the situation on the ground in Ukraine".
The ally said: "The foreign secretary has always talked about Nato in the context of it being a defensive alliance. Her point is that we stand by Article 5, and that we must do everything we can to help Ukraine short of putting boots on the ground.
"We take it very seriously and want to keep the situation calm."
It comes as Ukraine emerges from a weekend-long curfew, as shelling and blasts were heard in the capital and in cities across the country before dawn.
Shortly after the curfew was lifted on Monday morning, to allow residents to leave their homes and shelters to buy food and use public transport, air raid sirens could be heard across the city. The curfew will be reimposed between 10pm until 7am on Tuesday.
Ukrainian President Volodymyr Zelenskyy confirmed 16 Ukrainian children have been killed and another 45 injured in the days since the Kremlin launched its invasion.
British and US officials have played down Mr Putin's nuclear threat as it is unclear how his order changes Russia's nuclear posture.
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Russia maintains around 6,000 nuclear warheads, the most of any country in the world. NATO members France, the UK, and the US are also nuclear armed.
Prime Minister Boris Johnson dismissed the alert as a "distraction" from the struggle Russian troops are facing amid fierce resistance in Ukraine.
Defence Secretary Ben Wallace dismissed Putin's nuclear move as being a part of the Kremlin’s “battle of rhetoric” rather than a real threat.
He said the UK will "will not do anything to escalate in that area" and takes the threat "very, very seriously".
"But at the moment this is a battle of rhetoric that President Putin is deploying, and we just have to make sure we manage it properly," he told the BBC.