Update: Obama and Romney dined on chili and grilled chicken salad. They discussed America's leadership in the world and promised to stay in touch, according to a White House statement.

Former Massachusetts governor Mitt Romney will have lunch Thursday at the White House with President Obama in the private dining room, the White House announced. It will be their first meeting since the election; press will not be allowed.

A Romney aide called the lunch a gracious invitation from the president that the former GOP presidential challenger was glad to accept. Romney is also meeting with former running mate Rep. Paul Ryan while in town Thursday.

Obama promised in his election night victory speech that he would sit down with Romney "to talk about where we can work together to move this country forward." In a later press conference he elaborated, saying Romney "presented some ideas during the course of the campaign that I actually agree with. So it would be interesting to talk to him about something like that."

There has been speculation in the media that Obama might offer Romney a role in his administration, perhaps with the Commerce Department, giving Romney’s business background. But Carney said the president had no specific role in mind for the former head of Bain Capital, a private equity firm that Romney operated in the 1980s.

Since election night, Romney has all but disappeared from the public sphere. He has emerged only in photos taken by bystanders who spotted him pumping gas and visiting Disneyland. He has not tweeted since Nov. 10; his recent Facebook messages are about Thanksgiving

Obama met with Sen. John McCain (R-Ariz.) in Chicago shortly after McCain lost the 2008 presidential election. That meeting was private, as well, but photographers and a pool reporter were given a few minutes of access. 

Obama and McCain pledged after that meeting to "take on government waste and bitter partisanship." But their relationship quickly turned sour, with the Republican senator later saying he'd been snubbed.

David Nakamura and Philip Rucker contributed to this report.