"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," a spokeswoman for May's Downing Street office said.
The phone call between the two leaders came after last week's suspected chemical attack on a rebel-held Syrian town that killed at least 87 civilians.
Khamenei says US Syria strike 'strategic mistake'
Washington retaliated with an air strike on a Syrian air base, the first time the US has directly intervened against the Assad regime which it has blamed for the attack on civilians.
Britain said it "fully supported" the US strikes and both countries have put pressure on Russia to stop backing the Syrian regime, with British Foreign Minister Boris Johnson cancelling a visit to Moscow scheduled for Monday.
Johnson said his decision came after developments in Syria "changed the situation fundamentally" and that his priority would instead be the meeting of G7 foreign ministers on Monday.
The Italy summit of the seven major advanced economies was expected to be dominated by Syria, ahead of US Secretary of State Rex Tillerson travelling to Moscow on Tuesday for talks with his Russian counterpart Sergei Lavrov.
In their phone call on the eve of Tillerson's visit, Trump and May said it "provides an opportunity to make progress towards a solution which will deliver a lasting political settlement".
The Syrian regime has denied it was behind the April 4 attack in the town of Khan Sheikhun.
Russia, Iran army chiefs vow to continue Syria fight
Moscow has so far stood by Assad, describing the US strikes as inflicting "considerable damage" to already "lamentable" US-Russia ties.
Russia also threatened to suspend a vital hotline established to avoid mid-air collisions or clashes with a US-led coalition targeting the Islamic State group.
More than 320,000 people have been killed in Syria since the conflict erupted in March 2011 with anti-government demonstrations.
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