WASHINGTON — Senate Democrats on Tuesday blocked another vote on a resolution disapproving of the Iran nuclear deal, reprising the result of a vote last week.

Senator Mitch McConnell of Kentucky, the Republican leader, had called for a second vote despite protests from Democrats that it was a waste of time. Mr. McConnell insisted that senators needed to rethink their support for the accord, but 42 Democrats — the same number as last week — teamed to prevent the resolution from advancing.

Rather than give up, Mr. McConnell announced plans to force a vote on an amendment that would bar President Obama from lifting economic sanctions against Iran unless Tehran released American prisoners and recognized Israel as a state. Republican aides said that vote could take place Thursday morning.

Even Senator Chuck Schumer, Democrat of New York, who opposes the Iran deal, expressed frustration over the continuing debate. “The government is on the edge of shutting down,” he said. Noting that budget talks had yet to begin, Mr. Schumer waved his hand in a gesture of exasperation toward the Senate chamber, where his colleagues were still voting. “We’re doing this,” he said.