FILE - In this March 28, 2012 file photo, Sen. John McCain, R-Ariz. listens during a news conference on Capitol Hill in Washington. McCain said in an interview posted online Friday that "foreign money" was helping fellow Republican Mitt Romney's presidential hopes and singled out one of his ally's most generous supporters. (AP Photo/Jacquelyn Martin, File)
(AP Photo/Jacquelyn Martin, File)

Republican Sens. John McCain (Ariz.) and Lindsey Graham (S.C.) will meet with President Obama on Tuesday to discuss ongoing efforts to overhaul the nation’s immigration system, a White House official said Monday.

The one-time Republican presidential nominee first mentioned the possibility of a meeting with his 2008 rival while traveling in Mexico on Friday. McCain is the lead Republican on an eight-member bipartisan Senate working group attempting to craft immigration legislation, which also includes Graham.

The group, which includes four Democrats and four Republicans, unveiled a joint statement of principles last month to guide their efforts. They have said they hope to submit legislation in March.

Republicans on the committee had charged that the delicate talks were in danger of being derailed when a separate bill being drafted by the White House was leaked to the media more than a week ago. Obama officials immediately said they remained supportive of the Senate effort but were preparing their own legislation as a back-up in case Senate talks stall.

Still, Obama has been working ever since to repair ties to the group and assure it he seeks success from the bipartisan process. After McCain and others complained that Obama had met with the group’s Democrats but had not reached out to Republicans, the president called the Republican members of the group last week.

McCain said Monday that the meeting came at the president's invitation and he was pleased with the outreach.

"I’m encouraged anytime the president wants to talk to me," he said "I mean that."

This post has been updated.