He told reporters that Donald Trump had “expressed a great interest” in maintaining the US commitment to NATO.
During the campaign, Donald Trump said he might abandon a guarantee of protection for fellow NATO countries.
The Republican candidate’s statements alarmed the Baltic states, which fear Russian aggression.
Article 5 of the NATO treaty commits allies to come to the aid of a member state under attack.
In July, the Republican candidate said the US would only come to the aid of allies if they have “fulfilled their obligations to us”.
The US has long been pressing its European allies to spend more on defense.
President Obama was speaking hours before his arrival in Greece, on his final official overseas trip.
He will later travel on to Germany and then to Peru.
Security has been stepped up in the Greek capital Athens, where anti-US protests are planned.
Barack Obama is expected to use his final foreign visit to calm nerves over the forthcoming administration of Donald Trump.
Donald Trump’s surprise election victory has raised concern among some world leaders after a string of controversial statements he made during his campaign.
At a White House news conference on November 14, President Obama said Donald Trump had “expressed a great interest in maintaining our core strategic relationships”.
He said this included “strong and robust NATO” partnerships, which he said would convey “enormous continuity” to the world.
The president said that in last week’s White House meeting with his successor, he had urged Donald Trump to send “some signals of unity… and to reach out to minority groups or women or others that were concerned about the tenor of the campaign”.
President Obama said he “absolutely” had concerns about Donald Trump but urged his fellow Democrats to accept the result and “recognize that that is how democracy works”.
On November 15, NATO Secretary General Jens Stoltenberg expressed confidence about the Western alliance’s future.
“President-elect Donald Trump stated during the election campaign that he is a big fan of NATO, and I am certain that he will be a president… who will live up to all the commitments of the United States in the alliance,” he said.
Meanwhile, the Kremlin said on November 14 that President Vladimir Putin had spoken by phone to Donald Trump and agreed to work with him towards improving US-Russia relations.
Donald Trump has repeatedly praised Vladimir Putin, describing him as a stronger leader than Barack Obama.
Greek minister of state Nikos Pappas said there was surprise in Greece as elsewhere at the election result, but added: “Everybody would be expecting the US government to continue to be on our side.”
“The mood of Greek people for this political change is <<wait and see>>,” he said.
High on the agenda in talks between Barack Obama and PM Alexis Tsipras on November 15 will be Greece’s crippling debt problems.
The US and the International Monetary Fund (IMF) have urged restructuring of the debt but face resistance from EU states, particularly Germany.
As preparations for Barack Obama’s visit went ahead, Greek anarchist and left-wing groups announced they were planning protest marches “against the representative of imperialist powers”.
Police banned public gatherings in central Athens and near the city’s international airport until after Barack Obama’s departure. Extra officers are also being deployed.
The last official visit to Greece of a sitting US president – by Bill Clinton in 1999 – was marked by extensive violent protests.
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