Biden called Republican House Speaker Kevin McCarthy in Jerusalem, where he is on a diplomatic trip, to invite him to a May 9 White House meeting.
Biden also extended invitations to House Democratic leader Hakeem Jeffries, Senate Majority Leader Chuck Schumer and Republican leader Mitch McConnell.
Biden has steadfastly said he will not negotiate over the debt ceiling increase, but will discuss budget cuts after a new limit is passed.
A White House official said Biden, who had previously said he wouldn't meet McCarthy at all to discuss the debt limit, would "stress that Congress must take action to avoid default without conditions" on May 9.
The bill has no chance of passing the Democrat-controlled Senate and the White House has said Biden would veto the legislation if it did.