WASHINGTON — A measure that would force President Trump to win congressional authorization before taking further military action against Iran now has enough Republican support to pass the Senate, a key Democratic senator said Tuesday.

The senator, Tim Kaine of Virginia, said at least four Republicans would break ranks to pass a bill to curtail Mr. Trump’s war-making powers, underscoring growing dissatisfaction with the president’s Iran strategy among members of his own party. It would be a rebuke to the president as his impeachment trial gets underway and will most likely set up the seventh veto of his presidency.

The Republican defectors “were discouraged that the attitude that was being communicated to us was that Congress was an annoyance,” Mr. Kaine said. “After that, they came to me and we have been able to make some amendments.”

Senator Susan Collins of Maine, one of the Republicans who will support the measure, said in a statement that “Congress cannot be sidelined on these important decisions.” She said that although the resolution would continue to allow Mr. Trump to repel an imminent attack, “only the legislative branch may declare war or commit our armed forces to a sustained military conflict with Iran.”