WASHINGTON (CNN) -- Muslim and Jewish groups on Monday sharply criticized Sen. John McCain's comments that he would prefer a Christian president to lead the United States.

The Arizona Republican's remarks came in an interview with Beliefnet, a Web site that covers religious issues and affairs.

"I just have to say in all candor that since this nation was founded primarily on Christian principles, personally, I prefer someone who has a grounding in my faith," the GOP presidential hopeful told the Web site in an interview published Saturday.

McCain also said he agreed with a recent poll that 55 percent of Americans believe the U.S. Constitution establishes a Christian nation. "I would probably have to say yes, that the Constitution established the United States of America as a Christian nation," he said.

On Sunday night, McCain sought to clarify his remarks while campaigning in Hollis, New Hampshire. "What I do mean to say is the United States of America was founded on the values of Judeo-Christian values, which were translated by our founding fathers which is basically the rights of human dignity and human rights," he said.

"I believe that anyone can be president of the United States of any faith," McCain said, saying he was angry his remarks were misinterpreted but "there's nothing I can do about it."

Ibrahim Hooper, spokesman for the Council on American-Islamic Relations, said McCain's comments failed to recognize that Christianity is not the only faith with beliefs that support the concept of human rights.

"Sorry, Islam and other faiths have their basis in human dignity," Hooper said.

McCain's remarks also "go against the traditions of American pluralism and religious pluralism and inclusion," Hooper said.

Hooper's organization, a Washington-based Islamic civil rights and advocacy group, said it's trying to organize a group of Muslim leaders to meet with McCain.

The National Jewish Democratic Council, an advocacy group representing Jewish Democrats, also called on the Republican Party to denounce the remarks formally.

"Former maverick John McCain's statements were repugnant," the group's executive director, Ira N. Forman, said in a statement. "It's been sad watching him transform from political maverick to religious right mouthpiece."

Forman added, "Someone running for president ought to understand the Constitution a little better. Nowhere does it say the United States is a 'Christian' nation. How can we trust someone to uphold the Constitution who doesn't even know what is in it?"

McCain's communication director, Jill Hazelbaker, issued a statement Sunday defending her candidate's comments: "Read in context, his interview with Beliefnet makes clear that people of all faiths are entitled to all the rights protected by the Constitution, including the right to practice their religion freely.

"In the interview he also observed that the values protected by the Constitution, by which he meant values such as respect for human life and dignity, are rooted in the Judeo-Christian tradition. That is all he intended to say to the question, America is a Christian nation, and it is hardly a controversial claim." E-mail to a friend

CNN's Alexander Mooney, Sareena Dalla and Scott Anderson contributed to this report

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