Doug Stafford, Senator Rand Paul’s chief strategist, responded on Sunday night to Mr. Schatz’s idea: “We’ve being doing this one for years. Happy to help,” he wrote on Twitter. Mr. Paul has also been a longtime proponent of the demilitarization of local police and has previously teamed with Mr. Schatz to reform the Pentagon program, known as 1033.

It is unclear how much support Mr. Schatz’s measure could receive in the Republican-controlled Senate. But in the House, Representative Ruben Gallego, Democrat of Arizona and a former Marine, said on Monday that he would introduce similar legislation, opening up the possibility that the measure could find additional traction in making its way into the final defense bill.

“As a combat veteran and proud Marine, very little of my equipment or training was relevant to policing Phoenix or other American communities,” Mr. Gallego said. “Our neighborhoods aren’t war zones.”

The program was created in the 1990s in an effort to offload surplus military equipment and aid police departments during the war on drugs. It expanded in the wake of the Sept. 11, 2001, attacks but came under heavy scrutiny in the aftermath of a string of high-profile deaths of black men at the hands of the police, including the shooting of Michael Brown, an unarmed 18-year-old, by a white police officer in Ferguson, Mo., in 2014.

In response to stark images of heavily armed police confronting unarmed protesters in armored vehicles in Ferguson, Mr. Obama placed limits on that program in 2015, restricting the transfer of weapons, including battering rams and explosives, from the Pentagon to local police. The Pentagon reported in 2017 that 126 tracked armored vehicles, 138 grenade launchers and 1,623 bayonets had been returned since Mr. Obama prohibited their transfer.

But Mr. Trump rescinded those restrictions in 2017, opening the flow of equipment to police departments. He argued the gear was necessary for officers to protect themselves and their communities.

On his call with governors on Monday, the president appeared to applaud the National Guard’s handling of the riots in Minneapolis, pointedly remarking on their use of tear gas.