The Kremlin said the pair agreed to establish "partner-like cooperation" on issues such as Ukraine, Iran's nuclear programme and the Arab-Israeli conflict
In their first conversation since Mr Trump's inauguration, the Kremlin said in a statement that "both sides showed their readiness for active, joint work to stabilise and develop Russian-American cooperation".
The pair agreed to establish "partner-like cooperation" on issues such as Ukraine, Iran's nuclear programme, tensions on the Korean peninsula and the Arab-Israeli conflict, Moscow added.
There was no immediate comment from the White House on the eagerly awaited call.
The pair will maintain "regular personal contact" and start to prepare for a face-to-face meeting, the Kremlin statement added.
Ties between the US and Russia have been plunged to their lowest depths since the Cold War by the Ukraine crisis, Syria's civil war and allegations of Russian meddling in US elections.
Mr Trump has made it clear he wants to improve ties, provided he can get along with Mr Putin.
His stance on Russia has been intensely scrutinised by critics, who say the Republican was elected with help from Russian intelligence, a claim he denies.
There was no mention by the Kremlin of whether easing Western sanctions imposed on Russia over the Ukraine crisis had been discussed.
Ahead of the call, Mr Trump was non-committal on the subject, telling reporters on Friday: "We'll see what happens."
The European Union has also hit Russia with sanctions for its actions in Ukraine, while Prime Minister Theresa May said after meeting Mr Trump on Friday that sanctions should continue.