WASHINGTON — In a rare show of unity with President Obama, House Republican leaders will summon their fractious members back to the Capitol a day early next week to push through legislation to authorize the military to train Syrian rebels for the fight against Islamist militants.

The decision to bring lawmakers back on Monday, costing them a campaign day seven weeks before the midterm elections, showed how quickly the politics of Mr. Obama’s foreign policy shifted after he vowed in a speech to the nation on Wednesday night to degrade and ultimately destroy the Islamic State in Iraq and Syria. Speaker John A. Boehner, Republican of Ohio, and Senator Harry Reid, Democrat of Nevada, the majority leader, voiced strong support for the president’s appeal. Both men promised a quick vote to begin training rebels in the Free Syrian Army to take the ISIS fight into Syria.

“The president made clear he does not want boots on the ground,” Mr. Boehner said. “Well, somebody’s boots have to be on the ground,” he added, indicating that Iraqi troops and Syrian rebels would do that job. “At this point in time, it’s important to give the president what he asked for.”

Mr. Obama’s address, at least for now, accomplished one of its goals: a clear bipartisan resolve in Washington. Representative Peter T. King, Republican of New York, expressed concern that Mr. Obama was not laying out a real plan but instead delivering a “check-the-box speech” to answer critics who have called him weak and indecisive. Nevertheless, he said: “I am old school. I do support the commander in chief, so I will support him.”