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COLUMBUS, Ohio — Was Rick Santorum trying to imply that President Obama, who is Christian, actually responds to another theology?

At a campaign appearance here on Saturday morning, Mr. Santorum described the “president’s agenda” as being “not about you. It’s not about your quality of life. It’s not about your job.”

“It’s about some phony ideal, some phony theology. Oh, not a theology based on the Bible, a different theology. But no less a theology,” Mr. Santorum said, to wide applause.

His comments brought a swift rebuke from the Obama re-election campaign, which in the past has tended to focus more on attacks by Mitt Romney. Their quick attention may be an indication that Democrats believe Mr. Santorum’s momentum now means he stands a decent chance of defeating Mr. Romney for the Republican nomination and facing Mr. Obama in the general election this fall.

“This is just the latest low in a Republican primary campaign that has been fueled by distortions, ugliness, and searing pessimism and negativity,” Ben LaBolt, an Obama spokesman, said in an e-mailed statement. He also described Mr. Santorum’s comments as “a stark contrast with the president, who is focused every day on creating jobs and restoring economic security for the middle class.”

In comments later made to reporters here, Mr. Santorum was asked if he believes Mr. Obama was less of a Christian for — in Mr. Santorum’s view — “imposing his values” on the church.

“No one’s suggesting that,” Mr. Santorum said. “Obviously, as we all know in the Christian church there are a lot of different stripes of Christianity. I’m just saying he’s imposing his values on the church, and I think that’s wrong.”

He added, “If the President says he’s a Christian, he’s a Christian.”

Veiled suggestions that Mr. Obama is not a Christian — or not an American — have been an element of fringe politics since the last presidential election.

It go sot bad in 2008, in the opinion of Mr. Obama’s general election opponent that year, John McCain, that Mr. McCain took back the microphone from a woman at one of his rallies who asserted that Mr. Obama was “an Arab.” Mr. McCain then corrected the woman.

This year, Mr. Santorum has passed up similar opportunities to publicly correct misstatements about the president’s background.

Last month, a woman at one of Mr. Santorum’s campaign stops in Florida declared during a question-and-answer session that Mr. Obama was Muslim. According to an account by CNN, Mr. Santorum did not correct the woman’s statement, and he later said it is not his job to correct such statements.

“My position is clear, the president’s position is clear, I don’t think the president’s a Muslim, but I don’t think it’s my obligation to go out and repeat that every time someone who feels that way says something,” Mr. Santorum said on CNN, after that Florida appearance.