Theresa May and Donald Trump have agreed there is a "window of opportunity" to persuade Russia to abandon its support for Syrian leader Bashar al-Assad.
The two leaders spoke about the crisis by telephone, days after a US air strike against a Syrian airbase.
It comes after Boris Johnson told G7 leaders in Italy that further sanctions would be considered against Russia.
Foreign leaders there are trying to agree a co-ordinated response to Syria.
The meeting has been taking place ahead of a visit to Moscow by US Secretary of State Rex Tillerson.
Mr Trump ordered a series of missile strikes against a Syrian airbase on Friday in response to the deaths of more than 80 people, including children, during a chemical attack in the rebel-held town of Khan Sheikhoun on 4 April.
Mrs May said she agreed during a phone call that it was no longer in Russia's strategic interest to support President Assad.
'Lasting political settlement'
A Downing Street spokesman said Mr Trump thanked Mrs May, who is on a short walking holiday in Wales, for her support in the wake of the US air strike.
He added: "They agreed that US Secretary of State (Rex) 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 prime minister and president also stressed the importance of the international community, including China, putting pressure on North Korea to constrain the threat it poses."
German Chancellor Angela Merkel also agreed during a call with Mr Trump that President Assad should be held accountable, the White House said.
US officials say the airbase it targeted was used to launch a chemical weapons attack that killed dozens of civilians.
But Syria has denied using any chemical agents and Russia says the US has failed to provide evidence Syria has chemical weapons.
The US president's spokesman Sean Spicer said on Monday that further action would be considered in certain circumstances.
But Russia and Iran - Assad's two principal international backers - have warned that they would respond "with force" to any fresh attack on their ally.
Earlier, UK Foreign Secretary Mr Johnson said senior Russian military officers involved in co-ordinating Syrian military efforts could face international sanctions.
At a meeting of G7 foreign ministers in Lucca, Italy, Mr Johnson issued a fresh appeal to Russian President Vladimir Putin to abandon his backing for his Syrian ally.
He said Russian President Vladimir Putin was "toxifying the reputation of Russia by his continual association with a guy who has flagrantly poisoned his own people".
Mr Johnson also defended his decision to pull out of talks with his Russian counterpart Sergey Lavrov, saying it was important that Mr Tillerson had the "clearest possible mandate" when he went to Moscow to deliver the response of the G7.
Meanwhile, Mr Trump's son, Eric, said the US would not be "pushed around" by Mr Putin, the Daily Telegraph reports.
The president is not intimidated by Moscow's talk of war, his son said.
He insisted there was "no one harder" than his father if Russia chose to "cross us".