President Barack Obama will host Mitt Romney for a private lunch at the White House today, their first meeting since the Democratic incumbent defeated his Republican challenger in a bitterly fought election.

The encounter follows Obama’s post-election promise to engage with the former Massachusetts governor and consider his ideas.

It also comes amid Obama’s efforts to work out with congressional leaders a way to avoid a looming ‘‘fiscal cliff’’ that could push the US economy back into recession.

‘‘Governor Romney will have a private lunch at the White House with President Obama in the private dining room,’’ the White House announced on Wednesday, little more than three weeks after the November 6 election.

The talks will be a chance for Obama to look bipartisan at a time when he needs Republican cooperation in Congress, and for Romney to start rebuilding his political stature after leading his party to a disappointing election outcome.

The meeting will be sandwiched between a series of events this week in which Obama is making his case to Americans to raise taxes on wealthy Americans while extending tax cuts for the middle class — an approach that his former Republican rival strongly opposed during the campaign.

Obama’s Democrats and their Republican foes remain deadlocked over dramatic, year-end tax increases and spending cuts known as the fiscal cliff.

Fresh from his election win, Obama sought in his victory speech to show a willingness to reach across the political aisle when he offered to meet Romney ‘‘to talk about where we can work together to move this country forward’’.

Obama’s aides contacted Romney’s camp shortly afterward.

Their only encounters during the campaign — a series of three nationally televised debates — were fraught with tension, with the candidates exhibiting little personal chemistry.

ROLE FOR ROMNEY?

Despite that, Obama told a November 14 news conference he could envisage a future role in public service for Romney, though he had no specific ‘‘assignment’’ for him.

White House spokesman Jay Carney mentioned Romney’s management skills, demonstrated in his running of the 2002 Salt Lake City Olympics, and said Obama looked forward to discussing, among a variety of issues, the president’s ‘‘interest in making the federal government more efficient’’.

Obama earlier this year asked Congress for powers to carry out a major overhaul that would merge six trade and business agencies, a move that could ultimately unravel the sprawling Commerce Department.

Romney, in a conference call with donors after the election, was widely reported to have said that Obama won by using targeted initiatives to reward specific constituencies, including African-Americans, Latinos and young people.

Some of Romney’s fellow Republicans, eager to regroup after their disappointing election outcome, disavowed his comments.

When they sit down together, the event will be closed to the media.

‘‘We’re going to let the two men who spent a great deal of time in public eye over the course of the past year, both of them, have a private lunch together,’’ Carney said.

While in Washington, Romney will also meet with his former vice presidential running mate, Paul Ryan, according to a Ryan aide.

Obama, who won a decisive victory after a bruising campaign, had sought to depict Romney as out of touch with ordinary Americans and intent on shielding the rich from higher taxes.

Romney had accused Obama of failed economic policies and wasteful spending to promote big government.

- Reuters