Iran is exploiting the U.S. political campaign to continue advancing its nuclear program, Republican Sen. Lindsey Graham asserted Sunday.

"I think the Iranians are trying to take advantage of our election cycle to continue to talk," Graham said on "Fox News Sunday." "As we talk with the Iranians, whether it's bilaterally or unilaterally, they continue to enrich (uranium)."

Graham's comments came as The New York Times reported the U.S. and Iran have agreed to one-on-one talks about Iran's nuclear program, although, according to the paper, Iranian officials insisted the talks wait until after the U.S. presidential election. In a statement, National Security Council spokesman Tommy Vietor denied the U.S. and Iran have agreed to bilateral talks "or any meeting after the American elections."

Graham said "the time for talking is over" and blasted the Obama administration's policy of pursuing sanctions against Iran.

"The purpose of sanctions is to stop the Iranians from building a nuclear program. ... It's been a miserable failure," he said. "There is a pattern here: We talk, they enrich. It needs to stop. We need to have red lines coordinated with Israel and end this before it gets out of hand."

Democratic Sen. Dick Durbin, also on Fox, defended the Obama administration. "The sanctions regime that President Obama put together with Israel and many other countries around the world is putting pressure on Iran to sit down and finally acknowledge that they cannot have a nuclear weapon."

Republican Sen. Marco Rubio echoed Graham's assertion that Iran is using the idea of negotiations as a way to "buy time to further their nuclear program." Speaking on CBS's "Face the Nation," Rubio declined to comment directly on the New York Times story. But he did say, "I think Governor Romney would agree with this: Force is the last option. It's the least desirable one. It has to be on the table, and the candidates agree on that."