WATCH: Melania likes Michelle Obama, tweets Trump

US President-elect Donald Trump said his wife Melania likes First Lady Michelle Obama a lot following a transition meeting between them at the White House.

"A fantastic day in DC. Met with President Obama for first time. Really good meeting, great chemistry. Melania liked Mrs. O a lot!" Trump tweeted on Thursday night.

The tweet came after Michelle gave a traditional tour of the White House to Melania, who will succeed her as First Lady from January 20, 2017, Efe news reported.

The tour included a look around the private residence, the Truman balcony, the official reception area and the Oval Office, the White House Press Secretary Josh Earnest said.

The women also had tea together and talked about how to raise children in the White House. Melania's son Barron is 10, the same age as Michelle's oldest daughter Malia was when they moved into the presidential mansion.

"The meeting was a gesture of hospitality. Michelle Obama has publicly explained the stress of moving to a new place, living in a fishbowl, a museum, and I'm sure Melania Trump is feeling part of that same anxiety," said Earnest.

The connection between the two wives began before they got to know each other when Melania plagiarised a part of Michelle's speech during the Republican National Convention in July.

Although the plagiarism sparked a row, Trump himself joked about it at a charity dinner months later.

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"Michelle Obama gives a speech, and everyone loves it. It's fantastic. They think she's absolutely great. My wife, Melania, gives the exact same speech, and people get on her case! And I don't get it. I don't know why," he said. "This one's going to get me in trouble."

Melania, 46, will be an unquestionably atypical first lady, only the second to have been born outside the US. However, the former model still seeks to play the role in the most traditional way.

Obama is a very good man: Trump

Obama and Trump on Thursday put past animosity aside during a 90-minute White House meeting designed to quell fears about the health of the world's pre-eminent democracy.

As protests against the Republican property mogul's shock election rumbled across US cities and world capitals contended with a suddenly uncertain world order, Obama and Trump vowed to carry out a smooth transfer of power.

After a nasty campaign that culminated in the election of a 70-year-old billionaire and former reality TV star who has never held public office and who gained power on a populist platform, the message was: this is business as usual in a democracy.

The outgoing Democratic president and his successor huddled one-on-one in the Oval Office, for what Obama characterized as an "excellent conversation" and then put on a remarkably civil joint public appearance.

"It is important for all of us, regardless of party and regardless of political preferences, to now come together, work together, to deal with the many challenges that we face," Obama said.

Trump appeared more subdued than usual, and was unusually cautious and deferential in his remarks.

"Mr President, it was a great honor being with you," Trump said, calling Obama a "very good man."

The meeting, which came less than 36 hours after Trump's shock election victory over Democrat Hillary Clinton, had the potential to be awkward.

After all, Trump championed the so-called "birther movement" challenging that Obama was actually born in the United States - a suggestion laden with deep racial overtones - only dropping the position recently.

And if the president-elect fulfils his campaign promises, he will unravel almost all of Obama's signature achievements.

Trump - who previously called Obama the "most ignorant president in our history" - said he looked forward to receiving the president's counsel.

Obama - who previously said Trump was a whiner and "uniquely unqualified" to be commander-in-chief - vowed his support.

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