Democrats on Capitol Hill are forging ahead with efforts to curb President Trump’s ability to take further military action against Iran, moving amid a shaky cease-fire to build support for a measure that could come to a Senate vote as soon as the end of the week.

Senator Tim Kaine, Democrat of Virginia and the chief sponsor of a resolution that would require congressional approval before the U.S. military engages in further hostilities against Iran, proposed to narrow his measure to allay concerns that it could interfere with American support for Israel.

Mr. Kaine and two other Democratic backers of the resolution, Senators Adam Schiff of California and Andy Kim of New Jersey, introduced language on Tuesday specifying that the curb would only apply to offensive action, not for the United States’ continuing support for Israel “in taking defensive measures” against Iran or its proxies.

The amendment also would make explicit that congressional authorization would not be needed to defend against attacks on American personnel or facilities abroad or for the United States to continue sharing intelligence with allies like Israel in response to Iranian threats.

Mr. Schiff said in a statement that the changes were meant to clarify that the resolution would “not limit our ability to protect our troops or aid Israel in its own defense, should Iran continue to engage in attacks against us and our allies.”

The resolution stands little chance of approval. With Republicans holding majorities in both chambers of Congress, it is unlikely that any measure restricting Mr. Trump’s military authority will succeed. But by putting it forward, Mr. Kaine and other lawmakers who back such measures have reinvigorated a long-dormant debate over Congress’s role in matters of war.

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