Mr. Hawley supports repealing a decades-old law authorizing the use of military force in Iraq, which has been invoked as part of the legal justification for other military strikes since then and have 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 in 2002 to authorize the invasion of Iraq under President George W. Bush…

“I am a firm believer in Congress exercising its constitutional authority over war-making powers,” Senator Ted Cruz, Republican of Texas, said in a recent interview. But Mr. Cruz said he would be willing to repeal the Iraq authorization only if Congress granted the president new powers.

“If we clarify that there is ample authority to defend this nation from threats from Iran, then I’d be willing to support it,” he said.