Iran is trying to leverage the U.S. presidential election to its advantage, Sen. Lindsey Graham (R-S.C.) said Sunday morning, following a report that the two nations have agreed to negotiations over the Iranian nuclear program. 

“I think the Iranians are trying to take advantage of our election cycle to continue to talk,” Graham said in an interview on “Fox News Sunday.”

The New York Times reported Sunday that Washington and Tehran have for the first time agreed in principle to one-on-one negotiations over Iran’s nuclear program. The report said that Iranian officials insisted that talks wait until after the Nov. 6 election. A White House spokesman is quoted in the story as saying “It’s not true that the United States and Iran have agreed to one-on-one talks or any meeting after the American elections.”

“I think the time for talking is over,” Graham added.

Sen. Dick Durbin (D-Ill.), who appeared on the same program, took a different view from the South Carolina Republican. While Graham was critical of the Obama administration's approach to Iran, Durbin praised the sanctions regime Washington has pursued against the country, arguing the effort has had a positive effect.

"This month of October, the currency in Iran has declined 40 percent in value. 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," Durbin said. 

While Graham wasn't shy about weighing in on the New York Times report, another Republican senator wouldn't wade in too deeply Sunday. 

“I’m not going to comment on the story. The White House has denied it, and so there is really nothing to talk about,” said Sen. Marco Rubio (R-Fla.), on ABC’s “This Week With George Stephanopoulos.”

When asked on "This Week" whether now is the right time for direct talks with Iran, Rahm Emanuel, the Democratic mayor of Chicago and President Obama's former White House chief of staff, said it was not his call to make, and generally praised the president's approach. 

"That's not for me to say and they'll determine that," he said. "I don't have all the information. But I do know this, that three and a half years ago, we as a country, the world was criticizing us on Iran. Today, the world is criticizing Iran on its attempt to acquire nuclear weapons. That's a direct change.  The tables have been turned."

The back-and-forth over Iran came a day before the final debate between Obama and Republican challenger Mitt Romney was slated to take place Monday night in Florida. The debate will focus on foreign policy.

Updated at 11:55 a.m.