The Biden administration is open to several potential ways to tighten a much-stretched 2001 law that serves as the domestic legal basis for the open-ended “forever war” against terrorists around the world, a senior State Department official told Congress on Tuesday.

The Senate hearing on Tuesday repeatedly returned to the far more complicated question of what to do about the 2001 law, which has grown into the basis for sprawling global counterterrorism operations. Congress enacted the 2001 law to authorize war against those responsible for the Sept. 11 terrorist attacks.

But administrations of both parties have used it as the legal basis for military action against targets well beyond Al Qaeda and the Taliban in Afghanistan, including interpreting it to justify warfare against a Qaeda affiliate in Yemen, the Islamic State in Iraq and Syria, and Al Shabab in Somalia.

When Mr. Biden took office, he imposed new limits on counterterrorism drone strikes and commando raids away from conventional battlefields — places like Somalia and Yemen by generally requiring advance White House permission. And in April, he ordered a withdrawal of American ground forces from Afghanistan, saying that “it is time to end the forever war.”

However, after a six-month lull in American drone strikes in Somalia, the Pentagon in recent weeks has carried out three of them. Each time, it has claimed that the justification was “collective” self-defence of Somali partner forces battling Al Shabab, invoking an exception to Mr. Biden’s general policy requirement to seek White House permission ahead of time. Both Democrats and Republicans had something to say about this.