Donald Trump gave Vladimir Putin between ten to 12 days to move towards a ceasefire on his war in Ukraine.
He threatened new sanctions and possibly secondary tariffs, which would penalise countries for trading with Russia.
But the Russian president has repeatedly defied Trump’s deadlines and threats.
Speaking alongside Sir Keir Starmer outside the president’s golfing hotel in Turnberry, South Ayrshire, Scotland, he said of Putin’s war: “We thought we had it settled numerous times.
“And then President Putin goes out and starts launching rockets into some city like Kyiv and kills a lot of people in a nursing home or whatever.
“You have bodies lying all over the street, and I say that’s not the way to do it. So we’ll see what happens with that.”
Earlier this month, Mr Trump threatened to impose “very severe” tariffs on Russia if Putin did not agree a ceasefire within 50 days, with the deadline due to expire on September 2.
As he took press questions alongside Sir Keir on Monday, Trump said: "I am going to make a new deadline of about 10 or 12 days from today.
"There is no reason in waiting."
He stressed he was “very disappointed” with Putin, and emphasised the death toll from his invasion of Ukraine, including to Russian soldiers, with hundreds of thousands killed or wounded.
Last week, Downing Street said both men were “set to talk about their shared desire to bring an end to the barbaric war” and “reflect on progress in their 50-day drive to arm Ukraine and force Putin to the negotiating table”.
Meanwhile, the conflict in Ukraine continues, with Russian drone and missile strikes hitting the country’s north-eastern Sumy region on Sunday, wounding four people.
Russian officials also claimed to have shot down 150 Ukrainian drones, with one person killed and three others injured near St Petersburg.
Putin’s army has been gradually seizing more land in eastern Ukraine, but often while suffering heavy losses.
After coming to office for a second term in January, Trump appeared to side with Putin as he sought to end the war.
He had a showdown meeting in the Oval Office in the White House with Ukraine’s president Volodymyr Zelensky.
But the US president seems to have gradually turned against Putin as he has dragged his feet over ending the Ukraine war.
He suggested on Monday that he was getting tired of talking to the Russian president and seeming to make progress but then for fresh Russian attacks on Ukrainian towns and cities to be launched within days.
Trump and Sir Keir also discussed the growing humanitarian crisis in Gaza, with the president refusing to say children are starving in the strip of land besieged by Israel, but the Prime Minister stressed people in the UK were “revolted” by the hunger situation.
The US president also doubled down on his comments on immigration in Europe and took a swipe at London Mayor Sir Sadiq Khan.
Trump and Sir Keir also discussed the US-UK free trade deal.
