WASHINGTON — With Iran threatening that any new sanctions would scuttle its interim nuclear deal with the West, the Obama administration is fighting a fierce battle to convince skeptical Senate Democrats not to pass any new measures against Tehran.

The White House effort achieved some success on Tuesday, when Senator Tim Johnson, a South Dakota Democrat who is chairman of the Senate Banking, Housing and Urban Affairs Committee, said the administration had made a strong case for a “pause” in congressional action, and that he was inclined not to move sanctions legislation forward in his committee.

But other prominent Democrats, including Senator Charles E. Schumer of New York, support new sanctions, with deferred imposition, and Senator Harry Reid of Nevada, the majority leader, is said to be sympathetic.

At a congressional hearing, Secretary of State John Kerry pleaded with lawmakers to give the diplomatic efforts breathing space. He said the Obama administration opposed even a bill that deferred additional measures for six months, and would impose them only if Iran did not adhere to strict limits on its nuclear program. Instead, he pledged to petition Congress for tougher sanctions if the effort to negotiate a comprehensive nuclear accord with Iran falls short. “We are committed to asking you for additional sanctions if we fail,” Mr. Kerry told the House Foreign Affairs Committee on Tuesday. “We will need them.”