The two leaders spoke on the phone ahead of critical talks at the G7 summit in Italy at which the countries will try to persuade allies of the need for sanctions against Russia following a suspected chemical weapons attack that killed dozens in Syria.
A Downing Street spokesman said Mr Trump thanked the Prime Minister for her support in the wake of last week's US missile attack on the air base from which the chemical attack is believed to have been launched.
He said: “The Prime Minister and the President agreed that a window of opportunity now exists in which to persuade Russia that its alliance with Assad is no longer in its strategic interest.
“They agreed that US Secretary of State Tillerson's visit to Moscow this week provides an opportunity to make progress towards a solution which will deliver a lasting political settlement.
“They also discussed the broader Middle East, including the threat posed by Iran throughout the region.”
The pair also stressed the need for the international community – especially China - to put pressure on North Korea.
The last-ditch attempt by the UK and the US to avert a diplomatic crisis with Russia comes as Foreign Secretary Boris Johnson issued a fresh appeal to Mr Putin as he arrived at the G7 summit in Italy.
Mr Johnson warned that Russia is “contaminated” by the country's continued support for Assad and the country could find itself the target of sweeping international sanctions if it does not change track.
“We will be discussing the possibility of further sanctions, certainly on some of the Syrian military figures, and indeed on some of the Russian military figures who have been involved in co-ordinating the Syrian military efforts and are thereby contaminated by the appalling behaviour of the Assad regime,” Mr Johnson told reporters.
He added that the Russians now have to make clear once and for all which side they are on following the Assad regime’s presumed use of chemical weapons, which he said had “changed the game”.
“They have a choice. That choice is to stick like glue to the Assad regime - that toxic regime which poisons its own people and is indeed poisoning the reputation of Russia - or to work with the rest of world to find a political solution,” he said.
Mr Johnson defended his decision to pull out of talks with his Russian counterpart Sergey Lavrov to take part in the G7 talks, saying it was vital for Rex Tillerson to have the “clearest possible mandate” when he went to Moscow to deliver the summit’s response.
“I think it is very important in these circumstances for the world to present a united front and for there to be absolutely no ambiguity about the message,” he said.
Russia and Iran – Assad’s two principal international backers – have both warned they will respond “with force” to any further attacks on their ally.
Amid the escalating tensions, the Prime Minister’s official spokesman refused to be drawn on whether the UK would support fresh US military action, saying it was a “hypothetical question”.
Mr Trump’s spokesman Sean Spicer warned that further action would be considered if chemical weapons were used again by the Assad regime.
“When you watch babies and children being gassed, and suffer under barrel bombs, you are instantaneously moved to action.
“I think this President has made it very clear that if those actions were to continue, further action will definitely be considered by the United States.”
Reuters contributed to this report.