The president's press secretary said in a statement Obama will "meet separately with the Democratic and Republican caucuses in both the House and Senate."
"The president asked for the opportunity to speak to the caucuses about the priorities on his legislative agenda," the statement said, noting details of when the meetings will take place would be announced later.
Senate Minority Leader Mitch McConnell, R-Ky., said in a release Obama would get together with GOP senators for lunch March 14. He said the meeting was requested by White House Chief of Staff Denis McDonough.
"We have numerous challenges facing the country and Republicans have offered the president serious solutions to shrink Washington spending and grow the economy," McConnell said.
Obama, who last attended a Senate Republican Policy Lunch May 25, 2010, also invited a group of GOP senators to dinner Wednesday evening at a hotel near the White House. CNN and NBC News reported the list of invited senators includes Lindsey Graham of South Carolina, Bob Corker of Tennessee, Kelly Ayotte of New Hampshire, John McCain of Arizona, Dan Coats of Indiana, Tom Coburn of Oklahoma, Richard Burr of North Carolina, Pat Toomey Pennsylvania, Ron Johnson of Wisconsin and John Hoeven of North Dakota.
"I'm glad the president is doing it," McCain told CNN. "I think it's very helpful we have continued discussions."
Graham said, "When he reaches out we've got to reach back."
Mike Sommers, chief of staff to House Speaker John Boehner, R-Ohio, said Boehner's office has received a White House request for a meeting between Obama and House Republicans, and was "working to schedule that meeting," CNN said. A House Democratic leadership aide said the president has requested a meeting with House Democrats.
The meetings -- intended to discuss spending, immigration and gun control -- follow a series of telephone calls from Obama to congressional leaders as across-the-board federal spending cuts go into effect.