Putin "called to offer his congratulations on winning a historic election," according to a Trump statement. The two leaders discussed issues including shared threats, strategic economic issues and the historical US-Russia relationship.
The Russian President was one of the first world leaders to congratulate Trump last Wednesday, sending him a telegram about an hour after he had emerged the victor, but the two have not met nor had they spoken previously.
According to the Kremlin, Trump and Putin agreed on "the extremely unsatisfactory" state of relations between the two countries and "declared the need for active joint work to normalise them."
The two leaders said they would work to "bring them (bilateral ties) to the framework of constructive cooperation.
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Citing the Russian leader, the Kremlin statement added that this new relationship will be based "on the principles of equality, mutual respect and respective non-involvement in the other party's domestic affairs."
Officials are now working to arrange a personal meeting between the two leaders, the statement said.
During the US presidential campaign, senior American security officials accused Russia of hacking the computers at the Democratic National Committee headquarters and releasing emails that proved embarrassing to Hillary Clinton campaign. Putin denied any state role in the hacking.
Relations between the two countries have soured in recent years, despite President Barack Obama starting his eight years in office by calling for a "reset" with one of the US' long-term rivals.
Obama has also condemned Russia's intervention on the side of pro-Russian rebels in eastern Ukraine, while Russia's decision to grant whistleblower Edward Snowden asylum infuriated Washington.
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