WASHINGTON — A bipartisan group of lawmakers on Wednesday called for Congress to debate and vote on whether to authorize President Obama to take military action against Sunni militants in Iraq and Syria.

In a letter to Speaker John A. Boehner, the lawmakers — Representatives Barbara Lee of California and James McGovern of Massachusetts, both Democrats, and Walter B. Jones, Republican of North Carolina — said it was time for Congress to weigh in on whether to give Mr. Obama the power to broaden what began as a limited military mission in Iraq.

The number of American troops and airstrikes in Iraq has “increased significantly” while lawmakers have been on their August break, the three House members said, and the administration has begun weighing whether to expand the operation to Syria.

“We all share concerns about the Islamic State’s (IS) brutal tactics and further destabilization of the region,” the lawmakers wrote, adding that they also supported the Iraq mission that Mr. Obama announced on Aug. 7. “But current military operations now underway in Iraq appear to be beyond the scope of these limited purposes, and even greater expansion is under discussion.