WASHINGTON — President Barack Obama welcomed Sen. John McCain, R-Ariz., to the Oval Office on Wednesday for a rare face-to-face meeting between the two former rivals, covering issues such as immigration reform and the situation in the Middle East.

On the issue of Egypt, McCain had offered measured praise so far for Obama’s handling of the crisis, saying Sunday that he should do more to press for open elections.

After leaving the Oval Office, McCain used the social networking site Twitter to call for Egyptian President Hosni Mubarak to step down.

“”It’s in the best interest of Egypt, its people & its military,”” he said.

McCain’s office described the meeting as productive, saying the two also discussed border security, trade and budget issues.

“”Sen. McCain looks forward to working with the president to address issues of mutual concern for the welfare of our country in these challenging times,”” his office said in a statement after the senator left.

Earlier, press secretary Robert Gibbs singled out earmark reform as an issue where Obama and McCain have found common ground. When Obama said he would veto any legislation that included lawmakers’ pet projects, McCain was one of the few lawmakers applauding.

Wednesday’s meeting comes amid a thaw in the often-frosty relationship between the president and his 2008 rival. It dates back even before the last presidential campaign, when the new Illinois senator sought the veteran Republican’s cooperation on ethics reform but later split amid partisan wrangling over the issue in the campaign year of 2006.

The two quickly sought to put their divisive 2008 race behind them, with Obama feting McCain at a pre-inaugural dinner. But as the senator sought re-election in a climate where conservative activists were targeting longtime GOP incumbents, McCain emerged as one of Obama’s harshest critics. One of his first ads accused the president of engaging in an “”extreme left wing crusade to bankrupt America,”” and touted: “”I stand in his way every day.””

In the last month, however, McCain has praised Obama for his handling of the Tucson shooting aftermath and offered measured support for his approach to the Egypt crisis.

“”I disagree with many of the president’s policies, but I believe he is a patriot sincerely intent on using his time in office to advance our country’s cause,”” McCain wrote in a Washington Post opinion piece on Jan. 16.