During a phone call on Tuesday they agreed to try to meet up for face-to-face talks in Germany as they discussed working together to end the violence in Syria.
Last month US air strikes in Syria strained relations between the two countries.
The conversation has been described by the White House as "very good", while the Kremlin called it "business-like" and "constructive."
The White House said the two leaders agreed that "all parties must do all they can to end the violence" in Syria and that Trump and Putin also discussed working together against Islamic militants throughout the Middle East.
A White House statement said: “The conversation was a very good one, and included the discussion of safe, or de-escalation, zones to achieve lasting peace for humanitarian and many other reasons.”
Trump's decision to launch 59 cruise missiles against a Syrian airfield on April 4 in retaliation for a chemical weapons attack angered the Russians and led to some bitter exchanges between the two governments.
The White House statement said Washington will send a representative to Syrian cease-fire talks in Astana, Kazakhstan, on Wednesday and Thursday.
"They also discussed at length working together to eradicate terrorism throughout the Middle East. Finally, they spoke about how best to resolve the very dangerous situation in North Korea," the statement said.
A separate statement from the Kremlin suggested a face-to-face meeting is on the cards.
The two agreed to try to meet around the time of the G20 summit in Hamburg in July and work together to try to strengthen a shaky ceasefire in Syria, the Kremlin said in a statement.
The Kremlin said the two leaders had emphasised coordinating their actions to fight international terrorism.
On North Korea, the Kremlin said Putin called for restraint and that the two leaders had agreed to work together to make diplomatic progress there too.