The debate in Congress over presidential war powers will test a divided Republican Party.

When it comes to reining in presidential war powers, Senator Josh Hawley of Missouri, regarded as a leading prospect for the 2024 Republican nomination, agrees with President Biden.

Mr. Hawley supports repealing a 2002 law authorizing the use of military force in Iraq, which has since been invoked as part of the legal justification for other military strikes and become the initial focus of a broader effort to re-examine how much leeway Congress should give presidents to wage war.

“It’s time to kill this,” Mr. Hawley said of the law, passed to authorize the invasion of Iraq under President George W. Bush.

The senator, who has styled himself as former President Donald J. Trump’s populist heir, said it was a matter of listening to his party’s voters, whom he said want “to get out” of the nation’s wars.

His stance reflects a tentative but notable shift underway among Republicans as the United States haltingly disengages from what critics call the “forever wars” in Afghanistan and Iraq and continues to debate how to battle terrorist groups in the Middle East and Africa.

After espousing hawkish, interventionist positions for decades and almost uniformly backing the wars in Afghanistan and Iraq, the Republican Party is now grappling with political pressure to align itself more closely with the inward-looking “America First” foreign policy articulated by Mr. Trump and backed by many conservative voters.

Many Republicans remain opposed to repealing the Iraq-related authorization. And they have shown little enthusiasm for getting rid of the much broader war authorization passed by Congress after the Sept. 11 attacks, which has been used by successive administrations of both parties as the main legal basis for a wide range of military actions.

The shifting politics of the issue have helped to fuel the first significant bipartisan effort in a generation to curb a president’s authority to take military action.

The House, with support from dozens of Republicans, passed two bills in June repealing the Iraq measures, and on Wednesday, as a Senate committee approved legislation to repeal both, Senator Chuck Schumer, Democrat of New York and the majority leader, confirmed that he would bring it up this year.

Legislation taking shape in the Senate to repeal both a 1991 authorization for the Persian Gulf War and the 2002 law, an effort blessed by Mr. Biden, is partly symbolic, given that the government says it is not relying on either of them. But it reflects a growing consensus in favor of reasserting Congress’s influence over matters of war and peace, driven at least in part by the changing Republican political calculus.