Trump, Putin speak by phone, aim for 'constructive cooperation': Kremlin

US President-elect Donald Trump and Russian President Vladimir Putin have agreed to work towards "constructive cooperation", including on fighting terrorism, the Kremlin says.

In their first phone call since Trump won the Nov 8 election, they have agreed to "channel" relations between Russia and the United States and "combine efforts to tackle international terrorism and extremism".

"The importance of creating a solid basis for bilateral ties was underscored, in particularly by developing the trade-economic component," the Kremlin said in its statement on Monday.

Donald Trump in New Hampshire during primary campaigns. Reuters

Vladimir Putin speaks on the phone at his campaign headquarters in Moscow March 4, 2012. Reuters

It added that the countries should "return to pragmatic, mutually beneficial cooperation, which would address the interests of both countries as well as stability and safety the world over."

The two men will maintain contact by phone and seek to meet each other in person, the statement said.

Trump will take office on Jan 20, replacing Barack Obama whose relations with Putin have become tense over various issues including Syria and Ukraine.