US President Barack Obama on Wednesday vowed to work for a smooth transition of power to president-elect Donald Trump despite what he called their "significant differences".

The outgoing president said in a brief speech that he wished the Republican Trump well.

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

"Everybody is sad when their side loses an election, but the day after we have to remember we're actually all on one team. We're Americans first, we're patriots first, we all want what's best for this country."

Obama had campaigned heavily on behalf of defeated candidate Hillary Clinton, a fellow Democrat, often portraying the election as crucial to ensuring his legacy. Trump has promised to undo many of his top domestic and foreign policy initiatives.

Obama urged Democrats to put aside their differences and tried to strike a positive tone after what was a devastating defeat for his party.

"You have to stay encouraged. Don't get cynical," he said. "Don't ever think you can't make a difference."

Obama had previously warned voters that if Trump were to win, "all that progress goes down the drain".

Prior to his remarks, Clinton said in a concession speech that the United States was "more deeply divided than we thought," urging her supporters to accept the outcome of the presidential election.

"I still believe in America, and I always will," she said.