WASHINGTON — A personal missive by Senator McCain has failed to win over critics of his comments asserting that the Constitution established America “as a Christian nation.” In an exchange of letters obtained by The New York Sun, the Republican presidential hopeful accused the head of the Anti-Defamation League of misconstruing statements he made in an interview published Saturday with the Web site beliefnet.com.

Mr. McCain’s three-paragraph letter to the ADL’s national director, Abraham Foxman, amounted to an extended explanation of his remarks in the interview, during which he indicated he would support a Christian candidate over a Muslim for president and that “the Constitution established the United States as a Christian nation.” “You have misconstrued my interview with Beliefnet, in which I made repeated reference to ‘Judeo-Christian’ values that informed our founding fathers’ respect for human rights,” the Arizona senator wrote.

His letter was dated Monday, the same day that Mr. Foxman wrote to Mr. McCain urging him to “reconsider and withdraw” his comments, calling them inaccurate and ill-advised.

“I have always avoided seeking political gain by aggravating racial or religious divisions, and I regret the insinuation that I would,” Mr. McCain wrote. “Indeed, I don’t think you will find anything in my life and political record to suggest the contrary.” In a brief reply, Mr. Foxman said Mr. McCain did not go far enough. He wrote to Mr. McCain that while he welcomed the clarification, “nevertheless we are disappointed that you did not expressly retract your statement that ‘the Constitution established the United States of America as a Christian nation.'” In an interview yesterday, Mr. Foxman called Mr. McCain “a friend of the Jewish community” but said his statement was “mischievous.” “For him to let that stand is very disappointing,” he said.

Mr. McCain has historically had close ties with Jewish leaders and is known as a strong backer of Israel, but the prolonged dispute over his remarks could damage his support as he tries to resurrect a struggling presidential campaign.

Another Jewish leader, Rabbi David Saperstein of the Religious Action Center of Reform Judaism, yesterday joined Mr. Foxman in calling on Mr. McCain to explicitly repudiate his “Christian nation” statement. If he does not, Mr. Saperstein said, “I think it will be bewildering to many in the Jewish community.” “This does not reflect the kinds of sentiments I’ve heard him convey whatsoever,” Mr. Saperstein added, saying he had worked with Mr. McCain for many years and that he had “always been extraordinarily tolerant.” The American Jewish Committee, the National Jewish Democratic Council, and the Interfaith Alliance have also criticized Mr. McCain’s remarks in recent days.

The Arizona senator has sought to clarify his comments several times in recent days without rescinding them entirely. He contacted the Beliefnet Web site shortly after the interview to say he would vote for a Muslim candidate if he or she were “best able” to lead the country.

The McCain campaign declined further comment yesterday and referred to his letter to Mr. Foxman.

A national finance director for Mr. McCain who serves on the board of directors of the Republican Jewish Coalition, Lewis Eisenberg, said in an interview that Mr. McCain’s record “is impeccable.” “I don’t know that I would have expressed myself in the way he did,” Mr. Eisenberg said, adding that he had “great respect not only for John McCain but for Abe Foxman and others who expressed chagrin” at the senator’s remarks.

He said he was fully satisfied with Mr. McCain’s explanation. “It has now become a tempest in a teapot, and the tea has already been served,” Mr. Eisenberg said.

He also pointed to comments made in defense of Mr. McCain by Senator Lieberman of Connecticut, an independent who caucuses with the Democrats.

Mr. Lieberman, who is an Orthodox Jew, told the Associated Press on Monday:

“I have known John McCain very well for many years and I know that he does not have a bigoted bone in his body. I know that he is fair and just to all Americans regardless of their faith.” Mr. Eisenberg said: “I agree 100% with Joe Lieberman.” Mr. McCain’s rivals in the presidential race have largely stayed out of the flap. Leading Democratic and Republican candidates declined comment for this article. A former Tennessee senator who entered the Republican race last month, Fred Thompson, was asked Monday about Mr. McCain’s “Christian nation” remark and his statement saying he would prefer a Christian over a Muslim presidential candidate.

“Factually, the Judeo-Christian heritage of the United States is certainly factual,” Mr. Thompson said, according to the Associated Press, before cautioning against stereotypes.

“There are a lot of Islamic individuals and citizens of this country who are not radical, who are good citizens,” Mr. Thompson said. “I can’t say I would vote for or against anybody in any category.”