TEHRAN — A day after President Obama secured enough votes to ensure approval of the Iranian nuclear deal in the United States Congress, Iran’s supreme leader, Ayatollah Ali Khamenei, on Thursday ordered Parliament to vote on the agreement and threatened to cancel the pact entirely if the West merely suspended, rather than canceled, economic sanctions, state news media reported.

While the Iranian Parliament is expected to approve the agreement, the announcement nonetheless represented a setback for President Hassan Rouhani and his nuclear negotiators, who have long held that the deal should be ratified by the Supreme National Security Council, which Mr. Rouhani heads. Their fear is that a debate in Parliament will provide a platform for strident, archconservative opponents of the pact.

The head of Parliament, Ali Larijani, who has been visiting New York for an international conference for speakers of parliaments, said on Thursday that he expected more “drama” in his own legislature than in Congress over the nuclear deal.

Mr. Larijani said that a final decision was expected “in about a month,” which would most likely mean that it would not come before Mr. Rouhani arrives in New York for the annual meeting of world leaders at the United Nations General Assembly at the end of the month.