Gregory Korte

USA TODAY

WASHINGTON — The United States and Russia appeared to be inching toward mediating a cease-fire in the Syrian civil war Tuesday, as President Trump and Russian President Vladimir Putin spoke for their first known conversation since Trump ordered airstrikes on a Syrian air base last month.

The Syrian civil war dominated the discussion, the White House said, and the two leaders "agreed that the suffering in Syria has gone on for far too long and that all parties must do all they can to end the violence."

U.S. and Russian accounts of the Tuesday phone call between contained no hints of the usual friction points, and both sides generally agreed on the tone and substance of the exchange. (White House: "The conversation was a very good one." Kremlin: "The conversation was held in a business-like and constructive atmosphere.")

Putin even invited Trump to talk more — and to meet face-to-face when both leaders are in Hamburg, Germany for the G-20 summit of major economic powers in July. That meeting was almost certain to happen anyway, but the White House version of the phone call made no mention of a future meeting.

Mysterious rash of Russian deaths casts suspicion on Vladimir Putin

Despite Trump's entreaties to Putin during the presidential campaign, Syria has remained a source of tension. Russia supports the regime of Syrian President Bashar Assad, and senior U.S. officials have stopped just short of suggesting Russian complicity in a deadly sarin gas attack on civilians in northwestern Syria. Trump ordered airstrikes on a Syrian airfield in retaliation, giving Russian forces just enough notice to get out of the line of fire.

In their account on Tuesday, the Russians also said the leaders "agreed to enliven dialogue" between Secretary of State Rex Tillerson and Foreign Minister Sergey Lavrov as cease fire talks continue in Kazakhstan this week.

The two leaders also talked about what both sides called a "dangerous situation" as North Korea continues missile tests in defiance of international agreements.

It was at least the third conversation between the two leaders since Trump's inauguration.