This comes after Putin and US envoy Steve Witkoff met in Moscow on Thursday evening, after which the Kremlin said it shared the US's "cautious optimism" over a peace process.
Trump said in a Truth Social post that the talks provided "a very good chance that this horrible, bloody war can finally come to an end".
Ukrainian President Volodymyr Zelensky, however, accused Putin of trying to drag out talks to continue the war, while Sir Keir Starmer said the Russian president could not be allowed to "play games" with ceasefire proposals.
Follow live: Trump says US had 'good and productive' talks with Putin over Ukraine war
Earlier this week, Ukraine accepted the US-proposed ceasefire deal, which Russia is yet to agree to.
On Thursday, Putin had said the idea of a ceasefire was "right and we support it... but there are nuances" and he set out a number of tough conditions for peace, a response branded "manipulative" by Zelensky.
Ukraine's leader continued his criticism on Friday in a series of posts on X, writing: "Putin cannot exit this war because that would leave him with nothing.
"That is why he is now doing everything he can to sabotage diplomacy by setting extremely difficult and unacceptable conditions right from the start even before a ceasefire."
He said Putin would "drag" everyone into "endless discussions... wasting days, weeks, and months on meaningless talks while his guns continue to kill people".
"Every condition Putin puts forward is just an attempt to block any diplomacy. This is how Russia works. And we warned about this."
UK PM Sir Keir said the Kremlin's "complete disregard" for Trump's ceasefire proposal demonstrated Putin was "not serious about peace".
"If Russia finally comes to the table, then we must be ready to monitor a ceasefire to ensure it is a serious and enduring peace," he said.
"If they don't, then we need to strain every sinew to ramp up economic pressure on Russia to secure an end to this war."
On Saturday, Sir Keir will host a video call with as many as 25 leaders to develop the peacekeeping mission proposed during a summit in London earlier this month.
The "coalition of the willing" - as he called it - will work to deter future Russian aggression, should the US-proposed ceasefire come into effect.
In his social media posts on Friday, Zelensky "strongly" urged "everyone who can influence Russia, especially the United States, to take strong steps that can help", because Putin would not stop the war on his own.
"Putin is lying about the real situation on the battlefield... the casualties" and "the true state of his economy", he said, explaining that Putin was "doing everything possible to ensure that diplomacy fails".
But the White House believes the two sides have "never been this close to peace".
Talking to reporters, White House Press Secretary Karoline Leavitt maintained that the talks between Putin and Witkoff in Moscow on Thursday were "productive".
She added Trump has been "putting pressure on Putin and the Russians to do the right thing".
Trump's social media post also "strongly requested" Putin should spare the lives of Ukrainian troops, whom he described as surrounded by Russian forces, adding it would be a "horrible massacre" not seen since World War Two.
His comments came after Putin said on Thursday that Ukrainian troops in Kursk had been "isolated" and were trying to leave, as Russia ramps up efforts to reclaim the region invaded by Ukraine last year.
But on Friday, Ukraine's armed forces general staff denied the encirclement of its troops, calling it "false and fabricated".
In a statement, it said operations were continuing, with Ukrainian troops having withdrawn and "successfully regrouped" to better defensive positions.
"There is no threat of encirclement of our units," it said.
In response to Trump's request, Putin said Ukrainian soldiers in Kursk would be treated with "dignity in line with the norms of international law and the laws of the Russian Federation" if they gave up arms and surrendered.
Meanwhile, G7 members have been meeting in Quebec, where host Canadian Foreign Minister Mélanie Joly said all the members agreed with the US proposal of a ceasefire that is supported by Ukrainians.
"And we are now studying and looking at Russian reactions, so ultimately the ball is now in Russia's court when it comes to Ukraine."
UK Foreign Secretary David Lammy, who was also at the meeting, said the members were united in calling for a ceasefire with "no conditions".
Following the meeting, US Secretary of State Marco Rubio said the US would not make foreign policy decisions based on what leaders said on social media or at a news conference, and stressed the "only way to end this war is through a process of negotiations".
Vladimir Putin has said he agrees with the idea of a ceasefire in Ukraine, but that "questions" remain about the nature of a truce - as he set out a number of tough conditions for peace.
The Russian president was responding to a plan for a 30-day ceasefire, which Ukraine agreed to earlier this week following talks with the US.
Ukrainian President Volodymyr Zelensky described Putin's response to the plan as "manipulative" and called for more sanctions on Russia.
Meanwhile, the US placed further sanctions on Russian oil, gas and banking sectors.
Russian officials said Putin was expected to hold talks on the ceasefire on Thursday evening with US President Donald Trump's special envoy Steve Witkoff, who had flown to Moscow earlier that day.
It is not clear whether that meeting actually took place. On Friday, Russia's state media quoted the air traffic monitor Flightradar as saying the plane believed to be carrying Witkoff had left Moscow.
Speaking at a news conference in Moscow , Putin said of the ceasefire proposal: "The idea is right - and we support it - but there are questions that we need to discuss."
A ceasefire should lead to "an enduring peace and remove the root causes of this crisis", Putin said. "We need to negotiate with our American colleagues and partners," he said. "Maybe I'll have a call with Donald Trump."
Putin added: "It will be good for the Ukrainian side to achieve a 30-day ceasefire.
"We are in favour of it, but there are nuances."
One of the areas of contention is Russia's western Kursk region, Putin said, where Ukraine launched a military incursion last August and captured some territory.
He claimed Russia was fully back in control of Kursk, and said Ukrainian troops there "have been isolated".
"They are trying to leave, but we are in control. Their equipment has been abandoned," Putin said.
"There are two options for Ukrainians in Kursk - surrender or die."
Ukraine's top commander Oleksandr Syrskyi said a day earlier that Ukrainian troops would hold defensive positions in the Kursk region "as long as it is expedient and necessary" despite "increased" pressure from Russian forces.
At Thursday's press conference, Putin also outlined some of his questions over how a ceasefire would work. He asked: "How will those 30 days be used? For Ukraine to mobilise? Rearm? Train people? Or none of that? Then a question - how will that be controlled?
"Who will give the order to end the fighting? At what cost? Who decides who has broken any possible ceasefire, over 2,000km? All those questions need meticulous work from both sides. Who polices it?"
Putin "doesn't say no directly", Zelensky said in his nightly video address, but "in practice, he's preparing a rejection".
He added: "Putin, of course, is afraid to tell President Trump directly that he wants to continue this war, wants to kill Ukrainians."
The Russian leader had set so many pre-conditions "that nothing will work out at all", Zelensky said.
After Putin's remarks and Zelensky's response, there is now a clear divide between both sides' positions.
Ukraine wants a two-stage process: a quick ceasefire and then talks about a longer-term settlement.
Russia believes you cannot separate the two processes and all the issues should be decided in a single deal. Both sides seem content to argue their differences.
Ukraine believes it can put pressure on Russia, painting it as a reluctant peacemaker, playing for time. Russia, equally, believes it has a chance now to raise its fundamental concerns, about Nato expansion and Ukraine's sovereignty.
But this presents a problem for Donald Trump. He has made it clear he wants a quick result, ending the fighting in days.
And right now, Putin does not appear to want to play ball.
Getty Images President Trump wears a blue suit and red tie as he gestures while sat on a chair in the Oval Office at the White HouseGetty Images
Donald Trump has said he hopes Russia will "do the right thing"
Speaking at the White House following Putin's remarks, Trump said he would "love" to meet the Russian leader and that he hoped Russia would "do the right thing" and agree to the proposed 30-day truce.
"We'd like to see a ceasefire from Russia," he said.
Speaking earlier at a meeting in the Oval Office with Nato Secretary General Mark Rutte, Trump told reporters he had already discussed specifics with Ukraine.
"We've been discussing with Ukraine land and pieces of land that would be kept and lost, and all of the other elements of a final agreement," Trump said.
"A lot of the details of a final agreement have actually been discussed."
On the subject of Ukraine joining the Nato military alliance, Trump said "everybody knows what the answer to that is".
The fresh sanctions on Russian oil and gas came as the Trump administration further restricted access to US payment systems, making it harder for other countries to buy Russian oil.
Earlier in the day, Kremlin aide Yuri Ushakov rejected the ceasefire proposal put forward by the US.
On Wednesday, the Kremlin released a video it said showed Putin visiting Russia's Kursk region, symbolically dressed in military fatigues. Russia later said it recaptured the key town of Sudzha.
Russia launched a full-scale invasion in February 2022, and now controls about 20% of Ukrainian territory.
More than 95,000 people fighting for Russia's military have been killed in the war, according to data analysed so far and confirmed by the BBC. The actual death toll is believed to be much higher.
Russia's military has not publicly revealed its battlefield casualties since September 2022, when it said 5,937 soldiers had been killed.
Ukraine last updated its casualty figures in December 2024, when Zelensky acknowledged 43,000 Ukrainian deaths among soldiers and officers. Western analysts believe this figure to be underestimated.
