Russian President Vladimir Putin and US President-elect Donald Trump have spoken on the phone and agreed on the need to normalise ties between Washington and Moscow, the Kremlin said.
The Kremlin also said that the two politicians agreed to "make provisions for a personal meeting".
The presidential transition team in Washington said in a statement that it was Mr Putin who called Mr Trump tonight to "offer his congratulations on winning a historic election."
The Kremlin said that Mr Putin and Mr Trump noted "the extremely unsatisfactory state of Russian-US relations at present" and "declared the need for active joint work to normalise them."
Mr Putin wished Trump success in carrying out his campaign promises, the Kremlin said, and expressed his readiness to "create a dialogue of partnership with the new administration on the basis of equality, mutual respect and non-intervention in each other's domestic affairs."
They "agreed on the need to unite efforts in the struggle with the enemy number one: international terrorism and extremism," the Kremlin said, adding that in this context they discussed the "issues over resolving the crisis in Syria".
Mr Trump's team meanwhile said more generally that the pair discussed "the threats and challenges" facing both countries as well as economic issues and "the historical US-Russia relationship that dates back over 200 years."Mr Trump told Mr Putin he is looking forward to "a strong and enduring relationship with Russia and the people of Russia," the Washington statement said.
Meanwhile, US President Barack Obama has said it was important for President-elect Trump to send signals of unity after a bitterly fought campaign.
At a news conference, Mr Obama declined to comment on Mr Trump's selection of conservative provocateur Steve Bannon as his White House chief strategist.
But the Democratic president said he privately told Republican Mr Trump in an Oval Office meeting last week that because of the "bitterness and the ferocity of the campaign that it's really important to try to send some signals of unity and to reach out to minority groups, to women and others that were concerned about the tenor of the campaign".
Making his first appointments since last week's upset win over Democrat Hillary Clinton, Mr Trump picked Mr Bannon as his chief strategist, and Washington insider Reince Priebus as his chief of staff on Sunday, saying the two would share the task of steering his administration as "equal partners."
The choice of Mr Priebus was seen as a conciliatory signal of Mr Trump's willingness to work with Congress after he takes office.
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But critics blasted the selection of Mr Bannon, who spearheaded a shift of the Breitbart News website into a forum for the "alt-right," a loose online group of neo-Nazis, white supremacists and anti-Semites.
"There should be no sugarcoating the truth here: Donald Trump just invited a white nationalist into the highest reaches of the government," said Democratic Senator Jeff Merkley, who called on Mr Trump to rescind the choice.
Selection of Steve Bannon for senior WH role unsurprising but alarming. His alt-right, anti-Semitic & misogynistic views don't belong in WH
— Adam Schiff (@RepAdamSchiff) November 13, 2016
Mr Trump sought in his first televised interview as president-elect to reassure Americans fearful of a crackdown on minorities - while assuring his core supporters he will not let them down on gun rights, abortion or immigration.
The Republican billionaire, whose shock election on a populist and anti-immigration platform has spurred days of protests, told demonstrators they have no reason to fear his presidency.
"Don't be afraid. We are going to bring our country back," he said in the interview with CBS's '60 Minutes'.
Mr Trump said he was "saddened" by reports that incidents of harassment and intimidation of minorities had spiked since his election and called for it to end.
"I hate to hear that. I am so saddened to hear that," Mr Trump said when asked about the reports. "If it helps. I will say this, and I will say right to the cameras: Stop it."
A ‘surprised’ Donald Trump has told Americans to stop harassing minorities in the wake of his election win pic.twitter.com/IfrRaXgGVh
— RTÉ News (@rtenews) November 14, 2016
In the interview, Mr Trump sent out clear signals to his core electorate on a string of flashpoint issues.
He reaffirmed plans to aggressively deport or jail as many as three million undocumented immigrants - those with criminal records, he said.
Mr Trump also said he stood by his pledge to build a wall on the Mexican border, although he said it could include some fencing.
And on the key issue of the Supreme Court, where one of nine seats is currently vacant, he vowed his nominees would support abortion restrictions, and defend the constitutional right to bear arms.
"The judges will be pro-life," Mr Trump told CBS. "In terms of the whole gun situation," he added, "they're going to be very pro-Second Amendment."
But he also signalled that he would not seek to overturn the legalisation of same-sex marriage in the United States.
"It's law. It was settled in the Supreme Court. I mean it's done," Mr Trump said when asked if he supports marriage equality. "And I'm... I'm fine with that," he added.
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And in a final conciliatory gesture, the billionaire said he would forego the $400,000 salary that comes with the function of US president.
"I'm not going to take the salary. I'm not taking it," he said. "I think I have to by law take $1, so I'll take $1 a year," he added.
Since the election, Mr Trump has softened one of his major campaign promises, the vow to build a wall along the US border with Mexico.
In the CBS interview, which aired yesterday, Mr Trump said he would accept fencing instead of a brick-and-mortar wall.
"But certain areas, a wall is more appropriate. I'm very good at this, it's called construction, there could be some fencing," the New York property developer said.
Undocumented Irish 'must be normalised'
The Minister of State for European Affairs has said the issue of undocumented Irish people living in the US has always been of concern to the Government.
The status of the Irish in the US has been highlighted in the wake of the election of Mr Trump.
The deportation of millions of illegal immigrants to the US was one of Mr Trump's key campaign issues.
Speaking on RTÉ's Morning Ireland, Dara Murphy welcomed the fact that Taoiseach Enda Kenny will meet Mr Trump after he assumes office early next year.
Mr Murphy said there were strong bilateral ties between both countries and it falls to the Government to make the point that the status of those undocumented Irish, who have made their lives and homes in the US, must be normalised because they are "in the main, American".
Meanwhile, Mr Murphy has rejected claims a special meeting of EU foreign ministers about Mr Trump's election is a "whinge-o-rama."
British Foreign Secretary Boris Johnson used the term to describe what he feels is an unnecessary meeting.
Mr Murphy described the meeting as a "very constructive and balanced" session.
