Russian Foreign Minister Sergei Lavrov and U.S. Secretary of State Rex Tillerson spoke by phone on Saturday about the situation in Syria after the U.S. strikes on a Syrian air base, the Russian ministry said in a statement.
US President Donald Trump said the attack was a response to the alleged chemical weapon use in Syria's Idlib on Tuesday, which Washington blames on the Syrian government.
Lavrov and Tillerson agreed to continue the discussion of the Syrian settlement during a personal meeting next week during US Secretary's of State visit to Moscow.
On Friday, the USA fired 59 Tomahawk missiles at Shayrat Airbase from destroyers in the Mediterranean Sea in response to Tuesday's Assad regime chemical attack in Idlib that left some 100 men, women, and children dead and more than 500 injured.
Johnson said his priority was to continue contact with the United States and other countries to provide worldwide support for a ceasefire in the days leading up to the G7 meeting on April 10 and 11.
In January, Mr Johnson said Assad should be allowed to run for election to remain in power in Syria and warned that Britain may have to "think afresh" about how to handle the crisis after failing to live up to its mantra that dictator must go.
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Secretary of State Rex Tillerson says he sees no reason for retaliation from Russian Federation for USA missile strikes on a Syrian air base.
He said he planned to gather a group of other "like-minded partners" in order to "explore next steps soon". "He will visit Moscow as planned and, following the G7 meeting, will be able to deliver that clear and coordinated message to the Russians", he added.
According to reports, 89 people, including 33 children and 18 women, died in a suspected nerve agent attack in the Syrian rebel-held town of Khan Sheikhoun earlier this week.
Johnson called on Russian Federation to work with the rest of the worldwide community to "ensure the shocking events of the last week are never repeated".
Iran's president Hassan Rouhani argued the move meant "all the terrorists in Syria are celebrating this USA attack".