Opponents in Iran have been using the issue in an effort to unseat the moderates backing President Hassan Rouhani, whose government negotiated the pact with the United States, five other nations — Britain, China, France, Germany and Russia — and the European Union. Those five nations and the bloc have largely lifted their sanctions against Iran, including prohibitions on financial transfers and oil purchases.

“There will be aggressive posturing by the hard-liners within Iran,” Senator Chris Coons, Democrat of Delaware, said on Thursday. “I expect that Secretary Kerry will have to have a very difficult call with Zarif,” he added, referring to Secretary of State John Kerry and Mohammad Javad Zarif, the Iranian foreign minister, who was Mr. Kerry’s negotiating partner.

On Friday, the Iranian government described the Senate vote as a “violation” of the nuclear agreement, and the developments angered officials close to Mr. Rouhani, who has become the face of the deal and Iran’s outreach to the West.

The Iranian government has interpreted the agreement to mean that there will be no new sanctions as long as the deal is valid, and it regarded the vote as a serious breach of that accord. “We have an action plan for any situation,” said the Foreign Ministry spokesman, Bahram Ghasemi, “and are fully prepared to defend our rights effectively, strongly and wisely in any situation.”

While the Obama administration said the vote would not change anything, the extension of the sanctions authorization will give President-elect Donald J. Trump an easy opportunity to shatter the accord if he wishes. Vice President-elect Mike Pence said during the campaign that the deal would be ripped up, though Mr. Trump, in interviews with The New York Times earlier this year, suggested that he would try to renegotiate the terms, not destroy it.