US President Donald Trump and his Russian counterpart have made a "significant start" in fixing their countries' relationship, while agreeing to cooperate in fighting the Islamic State of Iraq and the Levant group, the White House said following an hour-long phone call.

The two leaders' first conversation since Trump's inauguration covered topics ranging from cooperation in defeating ISIL "to efforts in working together to achieve more peace throughout the world including Syria," the statement said.

In separate remarks, Putin's office said both leaders expressed readiness to cooperate "on a constructive, equitable and mutually beneficial basis".

The Kremlin statement said the conversation also covered the "main aspects of the Ukrainian crisis".

US relations with Russia were strained during President Barack Obama's term, following the Russian annexation of Crimea from Ukraine, prompting Washington to impose sanctions on Moscow.

The US and Russia have also been at odds over Syria, where Russia has provided extensive military support for its ally, President Bashar al-Assad.

Diplomatic relations were further strained after American intelligence agencies reported Kremlin hacked Democratic Party emails as part of a pro-Trump campaign to influence November's election.

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Since Trump's victory, Putin has praised the US leader and his policies.

The telephone conversation on Saturday came on an intense day of diplomacy for Trump, who had talks scheduled with other world leaders, including German Chancellor Angela Merkel and the leaders of Japan, France and Australia.

He also signed an executive order directing the Pentagon to submit a strategy within 30 days to defeat ISIL

Merkel call

Trump and Merkel stressed the "fundamental importance" of the NATO alliance to transatlantic ties in their first telephone conversation.

The alliance was vital in "ensuring the peace and stability of our North Atlantic community", the two leaders said, according to a separate statement released after the 45-minute chat.

Statements released by both sides after the call made no mention of the immigration ban, but Merkel's spokesman, Steffen Seibert, said on Sunday that Merkel had reminded Trump of his human rights responsibilities.

"The Geneva Refugee Convention calls on the international community to take in war refugees on humanitarian grounds," he said.



"The chancellor stressed this policy in yesterday's phone call with the US president."

Trump's executive order restricting travel and instituting "extreme vetting" of visitors from seven Muslim-majority countries puts him at odds with Merkel, whose embrace of Syrian refugees was praised by Barack Obama even as it created political problems for her domestically.