WASHINGTON — Senator John McCain of Arizona will return to the Senate on Tuesday, less than a week after announcing he had brain cancer, to provide a critical vote for Republican leaders who need to clear a procedural hurdle in their quest to repeal the Affordable Care Act.

In a statement on Monday night, Mr. McCain’s office said the senator “looks forward to returning” to work on several legislative priorities, including defense spending and sanctions against Russia, Iran and North Korea — as well as health care.

The Senate majority leader, Mitch McConnell of Kentucky, plans to move ahead with a vote on Tuesday to proceed with the health care repeal bill that narrowly passed the House in May. But he has struggled to come up with the votes to get to that first step. Mr. McCain is expected to vote in favor of taking up the House bill.