Starmer backs Zelensky after Trump 'dictator' claim
But Badenoch said Trump was "right that Europe needs to pull its weight" and called on Sir Keir to "get on a plane to Washington and show some leadership".
The row between Trump and Zelensky has increased the political jeopardy for Sir Keir, ahead of a high-stakes meeting with the US president next week.
The prime minister will travel to Washington DC for his first in-person meeting with Trump as he seeks to influence the American approach to ending the war in Ukraine.
Sir Keir has said he wants to use his meeting with Trump next week to discuss a "US backstop" that he says is necessary to deter Russia from attacking its neighbour again.
The prime minister has said he would be prepared to deploy British troops to Ukraine to help guarantee its security as part of a peace deal.
Speaking to BBC Newsnight, Andrei Kelin, the Russian ambassador to the UK, said Moscow would not accept troops from the UK or other European nations in Ukraine, even if President Trump approved it.
Kelin also questioned whether there could be a potential peace agreement without fresh elections in Ukraine.
Zelensky won a five-year term in 2019 and has remained in office because elections have been suspended since martial law was declared after Russia's invasion.
Asked if Russia would give back some of the territory it had seized from Ukraine, Kelin said: "Why should we? We have liberated these territories, upon which Russian people are living for centuries."
The UK and other European nations have been scrambling to respond to this week's rapid developments, almost three years after Russia launched its full-scale invasion of Ukraine.
The week started with diplomats from the US and Russian meeting in Saudi Arabia for talks aimed at ending the war.
The US was accused of sidelining European leaders, including Zelensky, by not inviting them.
Then on Tuesday, President Trump appeared to blame Ukraine for the war and suggested the Zelensky's popularity rating was as low as 4%.
It's unclear what source the president was citing as he didn't provide evidence. A survey conducted this month found that 57% of Ukrainians said they trusted the president, according to the Ukraine-based Kyiv International Institute of Sociology.
In his remarks on Wednesday, Trump warned Zelensky that "he is not going to have a country left" if he did not make peace.
In the UK, Liberal Democrat leader Sir Ed Davey said calling Zelensky a dictator "must be where the line is drawn".
He wrote on X: "It is my sincere hope that the whole political spectrum in the United Kingdom will speak with one voice in opposition to Trump's lies."
Tory MP and former cabinet minister James Cleverly said Trump was wrong about Zelensky and urged Foreign Secretary David Lammy to "say so", adding "his silence is deafening".
"The UK & USA must send the message that we don't let tyrants win!," he posted.
Former Prime Minister Boris Johnson has also waded into the war of words, posting to say "of course Ukraine didn't start the war".
He added: "Trump's statements are not intended to be historically accurate but to shock Europeans into action."
Earlier, UK Defence Secretary John Healey visited Norway's border with Russia with Norwegian defence minister Tore Sandvik.
Asked whether the UK agreed with Trump's suggestion that Ukraine "started it", Healey told reporters: "Three years ago, one country illegally invaded another, and since then the Ukrainians have been fighting for their freedom.
"They've been fighting for their future, and they still are.
"So whilst all the focus may be on talks, not even negotiations, our concern as defence ministers is that we're not jeopardising the peace by forgetting about the war."