British Prime Minister Theresa May and U.S. President Donald Trump agreed to try to persuade Russia to break ties with Syrian President Bashar al-Assad in a phone conservation on April 10, May's office said.
A spokeswoman for May said the two leaders expressed hope that progress towards a solution in Syria could come this week when U.S. Secretary of State Rex Tillerson visits Moscow.
"A window of opportunity now exists in which to persuade Russia that its alliance with Assad is no longer in its strategic interest,"the spokeswoman said.
"Tillerson's visit to Moscow this week provides an opportunity to make progress towards a solution which will deliver a lasting political settlement."
Russia has shown little inclination to split with its longtime ally Syria, which provides Moscow with some of its only air and sea bases in the Mediterranean region.
Although the Kremlin has said it can't control everything Damascus does, it so far has stood by Assad and expressed anger over last week's U.S. missile strikes on the Syrian airfield allegedly used to launch a deadly chemical attack on civilians in Syria.
Moscow maintains that the U.S. strikes caused little damage on the ground but inflicted "considerable damage" to the already "lamentable" state of U.S.-Russia relations.
Earlier on April 10, British Foreign Secretary Boris Johnson warned that the United States may launch more missile strikes against Syria, echoing a warning from the Pentagon.
"The United States will not passively stand by while Assad murders innocent people with chemical weapons, which are prohibited by international law and which were declared destroyed," U.S. Defense Secretary Jim Mattis said, noting that 20 percent of Assad's "operational" aircraft were destroyed by last week's cruise missile strikes on Syria's Shayrat airfield.
"The Syrian government would be ill-advised ever again to use chemical weapons," he said.
Johnson said the Group of Seven foreign ministers will discuss the possibility of placing sanctions on Syrian and Russian military officials over the incident at a meeting this week in Italy.
He said sanctions could target "figures who have been involved in coordinating the Syrian military efforts and are thereby contaminated by the appalling behavior of [Assad’s] regime."
Johnson suggested the new sanctions would be aimed at pressuring Russia to split with Assad for the first time in six years of civil war, saying Russian President Vladimir Putin has a choice: to continue backing the "toxic" Assad government "or to work with the rest of the world to find a solution for Syria, a political solution."
It is "time for Vladimir Putin to face the truth about the tyrant he is propping up," Johnson said.
Russia has so far stood strongly behind the Syrian government, which denies that it launched the April 4 nerve gas attack in the town of Khan Sheikhun, which killed at least 87 people.
Russia and Syria contend that Syrian planes bombarding the town set off nerve gas canisters which were being stored on the ground by Syrian rebel forces -- a contention that Western allies say is far-fetched.
Russia showed its displeasure with the U.S. attack by threatening to suspend a vital hotline to the Pentagon that was established to avoid mid-air collisions or clashes with a U.S.-led coalition targeting the Islamic State group in Syria.
Moscow did not cancel the Kremlin's previously scheduled meeting with Tillerson over the incident, however, though it said on April 10 that the U.S. diplomat will not be meeting Putin.