Theresa May and Donald Trump have agreed that "a window of opportunity" now exists to persuade Russia to break ties with Syrian President Bashar al-Assad.
The US president and British Prime Minister spoke on Monday evening, with Mr Trump thanking Mrs May for her support following the air strikes he launched against the Assad regime last week.
A Downing Street spokesman 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 (Rex) Tillerson's visit to Moscow this week provides an opportunity to make progress towards a solution which will deliver a lasting political settlement."
Mr Trump also spoke to Angela Merkel, the German chancellor and agreed with both European allies "on the importance of holding Syrian President Bashar al-Assad accountable", the White House said in a statement.
Trump administration officials said a week ago that they had abandoned the goal of forcing Assad to leave power.
However, the chemical weapons attack on Idlib province last Tuesday, which left at least 87 people dead including more than 30 children, had a "profound effect" on the US president and led him to order retaliatory air strikes against an Assad regime air base.
Rex Tillerson, the secretary of state, said, following the chemical attack, there was "no role" for Assad in governing Syria. He will visit Moscow on Tuesday with the aim of persuading Russia, Syria's key ally, to distance itself from the Assad regime.
Sean Spicer, the White House press secretary, on Monday said Mr Trump was open to authorising additional strikes on Syria if the use of chemical weapons continues in the country. He said that even the use of barrel bombs by the regime, which is a frequent occurrence, would necessitate action.
"The sight of people being gassed and blown away by barrel bombs ensures that if we see this kind of action again, we hold open the possibility of future action," he said.
In a further development, the US has concluded that Russia knew in advance of Syria's chemical weapons attack last Tuesday, officials said.
A Russian-operated drone flew over a hospital as victims of the attack rushed to get treatment, US officials said.
A Russian-made fighter jet bombed the hospital several hours later in what American officials believe was an attempt to cover up the use of chemical weapons. It remains unclear whether the jet was being flown by Russia or Syria.
However, US officials have now confirmed the drone was operated by Russia and cited its position over the site of the attack as proof that Russia must have known the chemical weapons attack was coming and that victims were seeking treatment.
The US claimed that 20 per cent of Syria's operational aircraft were destroyed in the strikes on the air base.
"The Syrian government has lost the ability to refuel or re-arm aircraft at Shayrat airfield and at this point, use of the runway is of idle military interest," James Mattis, the defence secretary, said in a statement.
"The Syrian government would be ill-advised ever again to use chemical weapons."
In their phone call, Mrs May and Mr Trump 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," the statement said.