By Jeff Mason and Roberta Rampton

WASHINGTON (Reuters) - U.S. President Barack Obama pledged on Wednesday 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, 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 Democratic 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.

"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.

(Additional reporting by Ayesha Rascoe and Doina Chiacu; writing by Roberta Rampton; editing by Grant McCool and Jonathan Oatis)