Obama on Trump victory: We are now all rooting for his success

US President Barack Obama has pledged to work for a smooth transition of power with president-elect Donald Trump, the Republican winner of Tuesday's election, who has promised to undo Obama's top domestic and foreign policy initiatives.

In brief remarks to reporters in the White House Rose Garden on Wednesday, Obama urged fellow Democrats to put aside their disappointment and tried to strike a positive tone after a devastating electoral defeat.

"It is no secret that the president-elect and I have some pretty significant differences," Obama said with a smile about Trump, who had long questioned whether Obama had been born in the United States and his eligibility for office.

"We are now all rooting for his success in uniting and leading the country," Obama said.

Obama and his wife, Michelle, campaigned hard for Democrat candidate Hillary Clinton to defeat Trump, acknowledging that the president's legacy on healthcare, climate change and financial reforms were on the line.

But Obama kept his remarks on Wednesday focused on ensuring a successful transition for Trump, noting that his Republican predecessor, former President George W. Bush, had done the same for him eight years ago.

US President Barack Obama and Vice President Joe Biden (L) turn away from the lectern after Obama spoke about the election results that saw Donald Trump become President-elect from the Rose Garden of the White House in Washington, Nov 9, 2016. Reuters

"Everybody is sad when their side loses an election, but the day after we have to remember that we're actually all on one team," Obama said.

"I want to make sure that handoff is well executed because ultimately we're all on the same team," Obama said.

President Obama also hoped the US tradition of people in power not using the criminal justice system against their opponents would continue, the White House said on Wednesday when asked about Trump's pledge to jail Hillary Clinton.

"We've got a long tradition in this country of ... people in power not using the criminal justice system to exact political revenge. ... The president is hopeful that it will continue," White House spokesman Josh Earnest told a news briefing.