(CNN) - Sen. John McCain, who has led the effort to discredit Susan Rice, the U.S. ambassador to the United Nations, said Sunday he was willing to listen to Rice's testimony if she's nominated to become the next secretary of state.
McCain has criticized Rice for her statements immediately following the September attacks at the U.S. Consulate in Benghazi, Libya, which Rice initially described as stemming from protests against an anti-Islam video. Later her remarks came under scrutiny as further information suggested the attack was a premeditated assault.
McCain, R-Arizona, has fronted the criticism of Rice, along with Sens. Lindsey Graham of South Carolina and Kelly Ayotte of New Hampshire. They, along with many other Republicans, have said they would block Rice's nomination if President Barack Obama chooses her to replace Hillary Clinton as secretary of state. Elevating Rice to a cabinet position within the administration would require a Senate confirmation.
On Sunday, McCain was asked on Fox News if there was anything Rice could do to change his resolve to block her potential nomination.
"Sure," McCain said. "I'd give everyone the benefit of explaining their position and the actions that they took. I'd be glad to have the opportunity to discuss these issues with her."
On Wednesday, Rice explained she was relying "solely and squarely on the information provided to me by the intelligence community" when she made her initial remarks on the attack in Benghazi.
"I made clear that the information was preliminary," Rice told reporters outside the United Nations. Obama has also defended Rice and criticized McCain's attacks in a news conference two weeks ago, calling Republican criticism of Rice "outrageous."
Graham, appearing on ABC on Sunday, said he didn't believe Rice was using the best intelligence possible when she made her initial appearances, and that her explanation of the attack had political motives.
"I don't believe the video is the reason for this. I don't believe it was ever the reason for this. That was a political story, not an intel story, and we're going to hold people accountable for a major national security breakdown three weeks before the election. That is our job," Graham said.
Sen. Joe Lieberman, an independent who caucuses with Democrats in the Senate, said he would also require further explanation from Rice before voting to confirm her as secretary of state.
"I don't feel that I know exactly what she was told before she went on TV that Sunday morning," Lieberman said on CNN's "State of the Union." "And I think we ought to find out before we decide on whether she's a good or bad public servant."
Last week, a spokesman for the director of national intelligence said the unclassified talking points that Rice used in her initial appearances following the Benghazi attack had been altered by the intelligence community before they were distributed to government officials.
Rep. Peter King - chairman of the House Homeland Security Committee and another Republican who has sharply criticized Rice - said the U.N. ambassador should have gathered her own research before appearing on Sunday morning shows to discuss the Benghazi attack.
"If she is sent out to speak to the American people on what happened in Benghazi, she is obligated to do more than look at three sentences, or five sentences, of unclassified talking points. That was basically a cover story," King said on NBC. He said Rice had "failed in her responsibility" to provide the public with an accurate assessment of the consulate assault, which left four Americans dead, including the U.S. ambassador to Libya.
"She had access to all of the sensitive top secret classified information. And she knew that the story she was giving out was not entirely true," King said.
McCain said Sunday the chronicle of the talking points from the intelligence community was "assuming the proportions of any other major scandal in this town."
"There are many layers to the onion, there's all kinds of questions that have been raised," McCain said.
CNN's Dana Davidsen contributed to this report.