The question of whether the United States should seek to engage Iran in one-on-one talks on its nuclear program joined the likely topics for Monday’s final presidential debate as supporters of President Obama and Mitt Romney jousted on Sunday over the issue.

The prospect of such talks was raised in an article published over the weekend by The New York Times that said Iran and the United States had agreed in principle to direct talks after the presidential election.

On Saturday, the White House denied that a final agreement on direct talks had been reached, while saying that it remained open to such contacts. On Sunday, the Iranian Foreign Ministry dismissed the report.

But if the report proved to be true, said a supporter of Mr. Romney, the Republican candidate, Iran’s motives should be seriously questioned.

“I hope we don’t take the bait,” Senator Lindsey Graham, Republican of South Carolina, said on “Fox News Sunday.” “I think this is a ploy by the Iranians” to buy time for their nuclear program and divide the international coalition, he said.

A supporter of Mr. Obama, Senator Richard J. Durbin, Democrat of Illinois, said on the same program that the tough international sanctions the president helped marshal against Iran might be bearing fruit exactly as hoped, forcing Iran to blink.

“This month of October, the currency in Iran has declined 40 percent in value,” Mr. Durbin, a member of the Foreign Relations Committee, said. “There is unrest in the streets of Tehran, and the leaders in Iran are feeling it. That’s exactly what we wanted the sanctions program to do.”

The Times, citing unnamed senior Obama administration officials, reported over the weekend that after secret exchanges, American and Iranian officials had agreed in principle to hold one-on-one negotiations between the nations, which have not had official diplomatic relations since the 1979 Islamic Revolution in Iran.

Iran’s foreign minister, Ali Akbar Salehi, denied on Sunday that any direct talks had been scheduled. “We do not have anything such as talks with the United States,” he told the semiofficial Fars news agency.

Mr. Salehi predicted that there would be a new round of talks in November with the five permanent members of the United Nations Security Council — including the United States — and Germany, but said that “there is no fixed date yet.” Several rounds of such talks have failed to produce a breakthrough. The United States and its partners say Iran’s nuclear program is aimed at producing a weapon, but Iran says the program is for peaceful purposes.

Weighing in on the topic from Israel, Prime Minister Benjamin Netanyahu said Sunday that although he did not know whether the United States and Iran had discussed the possibility of direct negotiations, “very sharp sanctions and a credible military option” were the best means to halt Tehran’s nuclear program. He said Iran had used earlier multinational talks “to drag its feet and to gain time” to advance its weapons program.