The 55-year-old Obama has chosen the "cradle of democracy" Greece to deliver a speech addressing the uncertainties that have led to the rise of populists like Trump.
Obama met with Kountoura on Tuesday at a dinner hosted by Greek President Prokopis Pavlopoulos during which he pledged: "You will always have the support and the friendship of the United States, as you work to move the country ahead".
Obama is making his sixth and final visit to Germany as a sitting president this week, but he says he'd like to come back as a former president to attend Octoberfest.
US President Barack Obama has issued a warning against "crude nationalism" in the wake of Donald Trump's victory, saying the NY billionaire had tapped into a "troubling" strain of rhetoric playing on Americans' fears of globalisation to win the presidency.
While Obama was receptive to Greece's woes and repeated his belief that debt relief is necessary - though also stressing Greece must continue implementing painful reforms it signed up to in return for successive global bailouts - it is questionable how much of this stance will also be adopted by his successor, Donald Trump, following the latter's recent election victory.
Protesters threw Molotov cocktails, and police responded with stun grenades and tear gas, dispersing the crowds who eventually retreated into the side streets.
On other issues, Obama said he hoped for continuity of U.S.
He said leaders should heed lessons from election results in the United States and in Britain, which voted in June to exit the European Union. "We have very different points of view, but American democracy is bigger than any one person".
Obama insisted that people deserve the right to choose their governments and leaders.
Greek Prime Minister Alexis Tsipras won elections past year on what critics say was a populist platform, though one on the left of the political spectrum. He pushed his formerly small party to the forefront by telling Greeks tired from six years of financial crisis that he would reject austerity measures imposed in return for bailouts. Obama passed through the Propylaea, the monumental gateway that serves as an entrance to the site, and walked along the Parthenon temple, which is dedicated to the goddess Athena, considered the patron of Athens.
The entire site was closed to the public for Obama's visit, which has played out amid stringent security measures.
Greece's government hoped Obama would help persuade some of Greece's more reluctant worldwide creditors to grant debt relief, and pressure other European countries to share more of the burden of the continent's refugee crisis.
It's the final stage for Obama's two-day stop in Athens, where he was the first USA president to visit in 17 years.
Obama was receptive to Greece's woes and repeated his belief that debt relief is necessary. He said Greece must continue putting in place painful reforms it signed up to in return for successive global bailouts. It is questionable how much of this stance will also be adopted by Trump. Many have passed through Greece on their way to Europe, and Obama has called for countries to accept more refugees in an attempt to alleviate the crisis. Many are living in poor conditions in massively overcrowded camps.
"I've been clear from the beginning of this crisis that in order to make reforms sustainable, the Greek economy needs the space to return to growth and start creating jobs again", Obama said.
Speaking in Athens, Obama says "only a truly collective response by Europe and the world" can handle the hundreds of thousands of refugees fleeing violence in the Middle East. Traveling this week to Greece, Germany and Peru, Obama has tried to reassure USA partners that Trump, in their Oval Office meeting, expressed a "full commitment" to North Atlantic Treaty Organisation.