WASHINGTON (Reuters) - U.S. President Barack Obama met with a frequent critic, House Speaker Paul Ryan, on Tuesday as the political leaders searched for areas where they may be able to overcome partisan divisions.

Slideshow ( 4 images )

The Oval Office discussion was the Democratic president’s first formal face-to-face meeting with Ryan since the Wisconsin congressman took over the top post in the Republican-dominated House of Representatives in October. Following the meeting, which was closed to the press, the two ate lunch together in the White House.

The session marked a rare public detente between Obama and Ryan, who have repeatedly clashed over issues such as gun control and immigration reform. The get-together in the Obama’s office also included the Republican-controlled Senate’s majority leader, Mitch McConnell of Kentucky.

While the leaders said they hoped to find common ground, there were already signs on Tuesday that compromise might be elusive.

Sniping between the administration and the Republicans resumed just hours after the meeting, as White House Chief of Staff Denis McDonough slammed Republicans’ latest attempt to overturn the Affordable Care Act.

“Groundhog’s Day is great for a movie plot, not a legislative strategy,” McDonough said on Twitter in response to a post from Ryan’s account. “Groundhog Day” is a 1993 movie about a man who relives the same day over and over again.

During the meeting Obama urged actions in areas where Republicans had signaled some support, including ratifying the Trans-Pacific Partnership trade deal, providing tools to help address Puerto Rico’s fiscal crisis and advancing cancer treatment.

McConnell told reporters after the meeting that he had “some problems” with the trade pact and said he thought it should not be pursued before the November U.S. presidential election.

Ryan also raised concerns about the trade deal, his office said in a statement.

White House spokesman Josh Earnest said after the meeting that the administration does not have a specific timeline for Congress to act on the trade agreement, but lawmakers should act “quickly” once the pact is ready for consideration.

The leaders also discussed taking action to combat opioid addiction, criminal justice reform and the fight against the Zika virus.

Obama was pleased to meet with the Republican leaders, Earnest told reporters.

Despite the divisiveness seen on the campaign trail, “it actually is possible for leading Republicans to sit down in the same office with a leading Democrat and have a conversation about the priorities of the country,” he said.