Barack Obama and Mitt Romney discussed America’s leadership in the world at White House lunch

Barack Obama has met defeated Republican presidential candidate Mitt Romney for a private lunch at the White House.

Barack Obama and Mitt Romney discussed “America’s leadership in the world” and how to preserve it, the White House said.

Mitt Romney left after just over an hour and the two said they would stay in touch.

Meanwhile, negotiations over a looming “fiscal cliff” seemed to falter in Congress.

House Speaker John Boehner said no major progress on a deal had been made.

Barack Obama and Mitt Romney dined on white turkey chili and south-western grilled chicken salad during Thursday’s lunch meeting.

White House spokesman Jay Carney told reporters at a news briefing: “Governor Romney congratulated the president for the success of his campaign and wished him well over the coming four years.

“The focus of their discussion was on America’s leadership in the world and the importance of maintaining that leadership position in the future.

“They pledged to stay in touch, particularly if opportunities to work together on shared interests arise in the future.”

Barack Obama is also said to have noted that Mitt Romney’s “skills-set” could help improve the workings of the government.

Mitt Romney has spent the past three weeks mainly at his family’s California home, making no public appearances, although he was photographed on a family trip to Disneyland.

On election night, 6 November, Barack Obama pledged to meet the former Massachusetts governor for talks on how to “move this country forward”.

The pair sparred in a bitter campaign and are said to have little rapport.

On Thursday John Boehner, the top Republican in Congress, met Treasury Secretary Timothy Geithner to discuss the combination of tax rises and spending cuts due to take effect on 1 January 2013.

“No substantive progress has been made between the White House and the House,” John Boehner said after the meeting.

“I was hopeful we’d see a specific plan for cutting spending, and we sought to find out today what the president really is willing to do.”

Mitch McConnell, the top Republican in the Senate, said the Obama administration had taken a step “backward” away from consensus, after his meeting Timothy Geithner on Thursday.

Congressional Democrats countered that they had already outlined their party’s position, and said Republicans had not identified specific spending cuts.

Senate Majority Leader Harry Reid said: “We’re still waiting for a serious offer from Republicans.”

Some Republicans have said they would consider increased tax revenue as part of a deal to avoid the fiscal cliff.

But the White House believes that simply ending tax deductions would not generate enough new revenue to address the yawning budget deficit.

The fiscal cliff, which would suck about $600 billion out of the economy, could tip the US back into recession, analysts warn.

The measures were partly put in place within a 2011 deal to curb the yawning US budget deficit, but also include the expiration of Bush-era tax cuts for all Americans.