But in separate post-election remarks on Wednesday, both men appeared to seek to help the country heal from a bitterly divisive campaign, and that tone continued into the White House meeting. "He's- he explained some of the difficulties, some of the high-flying assets, and some of the really great things that have been achieved". "I very much look forward to dealing with the president in the future, including counsel".
While Trump noted that he and Obama had never met before, their political histories will forever be linked. That birther movement questioned the president's place of birth and thereby the legitimacy of the first African American president. Demonstrators from New England to the West Coast vented against the election victor on Wednesday, chanting "Not my president", burning a papier mache head of Mr Trump, beating a pinata with his likeness and carrying signs that said "Impeach Trump".
In one tweet that was recently deleted (but can be seen here and here), Trump even called for revolution, saying of Obama: "He lost the popular vote by a lot and won the election".
Obama said he had offered assistance to Trump over the next couple of months, and urged the country to unite to face its challenges.
JOSH EARNEST, White House Press Secretary: I feel confident in telling you that they didn't resolve all their differences. He says he plans to undermine key Obama policies, including the health care reforms, environmental regulations, protection of some immigrants from deportation, and the Iran nuclear deal.
Melania Trump and Michelle Obama also met on Thursday for the first time.
However, the picture was not taken on Thursday morning, but on Wednesday as Obama spoke in a live televised address after Democratic presidential candidate Hillary Clinton conceded to Trump. "The American people chose his successor".
Republicans were emboldened by Mr Trump's victory over Hillary Clinton, giving the Republican control of the White House and both chambers of Congress. This was a meeting that was going to last for maybe 10 or 15 minutes, and we were just going to get to know each other.
President-elect Donald Trump is keeping America in the dark about his earliest conversations and decisions about his incoming government, and bucking a long-standing practice meant to ensure the public has a watchful eye on the nation's new leader.
Cuba announces nationwide military drill after Trump win
The United States broke off diplomatic relations with Cuba in 1961 and placed an official embargo against the country in 1962. Later, to win the votes of Cuban American Republicans in South Florida, he promised to reverse the Obama opening.
Also on Trump's schedule was a meeting with House Speaker Paul Ryan, R-Wis., to discuss the GOP legislative agenda. "Big league jobs", he told the press.
Demonstrators break a shop window during a protest against the election of Republican Donald Trump as President of the United States in Portland, Ore.
His blunt call to ban all Muslims from entering the country, for example, was temporarily expunged from his campaign website after lingering there since he issued it in December, following the deadly terrorist attack in San Bernardino.
If Mr Trump makes good on his campaign promises, he will wipe away much of what Mr Obama has done during his eight years in office.
Speaking to Clinton supporters in October, following the release of tapes which showed Trump boasting about grabbing women "by the pussy", Mrs Obama said the tapes had "shaken [her] to [her] core". National security planning was being led by former Michigan Rep. Mike Rogers, who previously worked for the Federal Bureau of Investigation.
The White House, for example, did not arrange for the traditional photo op between the current first couple and the incoming one.
Mr Trump has 70 days to prepare for inauguration, assembling his cabinet, putting together a White House team and adding detail to what was a thin election manifesto.
"This decision could leave Americans blind about his whereabouts and well-being in the event of a national crisis", said Jeff Mason, White House correspondent for Reuters and the group's president.