The Senate on Friday blocked a Democratic resolution that would have forced President Trump to go to Congress for approval of further military action against Iran, dealing a blow to efforts to rein in his war powers.

The 53-to-47 vote against bringing up the resolution, mostly along party lines, came nearly a week after the president unilaterally ordered strikes against three Iranian nuclear facilities without consulting the House and Senate. It also followed a searing debate on the Senate floor over the role of Congress in authorizing the use of military force.

The measure, sponsored by Senator Tim Kaine, Democrat of Virginia, invoked the War Powers Act, a 1973 law aimed at limiting a president’s power to enter an armed conflict without the consent of Congress. It would have required the White House to notify lawmakers and seek the approval of both the House and Senate before U.S. forces could take further military action against Iran.

Earlier this week, Mr. Kaine said that if the Senate voted to take up his resolution, he would modify it to include language that affirmed the president’s authority to act in self-defense. He clarified that it did not limit U.S. support for Israel or any “defensive measures” it might take against Iran or its proxies. That was in part an effort to unite Democrats around the measure, even though the party is deeply divided over supporting Israel.

Still, the resolution had little chance of success in a Republican-led Congress that has split bitterly along partisan lines over the strikes, with most G.O.P. lawmakers — even anti-interventionists on the far right — supporting Mr. Trump’s actions, and many Democrats outraged about them.