Sen. Lindsey Graham (R-S.C.) said Sunday that Defense Secretary nominee Chuck Hagel sent him a letter disavowing a comment about Israel and the State Department that he allegedly made in 2007.

"I got a letter back from Sen. Hagel in response to my question, did you say that, and do you believe that? And the letter said he did not recall saying that. He disavows that statement," Graham said on "Fox News Sunday."

Graham was referring to a 2007 blog post indicating that in a speech at Rutgers University, Hagel said the State Department had become adjunct to the Israeli Foreign Minister's office. The South Carolina Republican appeared satisfied with Hagel's disavowal of the remark, barring new developments.

"Well, if in fact that's true, that would end the matter," Graham said, adding, "I just take him at his word unless something new comes along."

Graham was among the Republican senators who last week blocked Hagel in the nomination process, denying him of the 60 votes necessary for the Senate to proceed to a final confirmation vote. Another vote has been scheduled for Feb. 26, and since that would allow more time to examine Hagel's record, Republicans have signaled a willingness to allow a vote in which a simple majority would be enough for him to be confirmed.

Another Republican senator who voted to stall Hagel's confirmation is Sen. John McCain (R-Ariz.). On NBC News' "Meet The Press," McCain expressed confidence that Hagel would eventually win confirmation, even as he opposes President Obama's choice to head the Pentagon.

"We will have a vote when we get back, and I am confident that Senator Hagel will probably have the votes necessary to be confirmed," McCain said.

Graham called Hagel "one of the most unqualified, radical choices for secretary of defense in a very long time." But he nonetheless expressed openness to letting the Senate proceed to a vote on his confirmation, saying he gives Obama "great discretion."

White House Chief of Staff Denis McDonough said there isn't any reason for Republicans to hold up up Hagel's confirmation.

"It's a grave concern," McDonough said on ABC News' "This Week With George Stephanopoulos." "If you look at Chuck Hagel, decorated war veteran himself, war hero. Republican senator. Somebody who over the course of the last many years, either as a Republican senator or as the chairman of the president's Intelligence Advisory Board, I've worked with very closely.  This guy has one thing in mind, how do we protect the country.