Texas Gov. Rick Perry was supposed to be answering questions about his presidential bid. Instead, he raised more.

Perry tried to reboot his struggling campaign this week by announcing a broad economic policy agenda, recruiting longtime strategists with national credentials and reintroducing himself as the “bold” choice for the Republican nomination. But he undercut the reach of his economic message by repeatedly injecting an issue that most Americans thought had been put to rest.

Perry cast doubt about President Obama’s birthplace, Hono­lulu, suggesting in two interviews this week that Obama may have been born outside the United States. If true, that would make his presidency illegal. This spring, as would-be candidate Donald Trump rocketed in opinion polls partly by pushing “birther” conspiracies, Obama publicly released his long-form birth certificate to prove that he was born in Hawaii.

In an interview with Parade Magazine published Sunday, Perry said he does not know if Obama’s birth certificate is authentic. He continued to press that point in an interview with John Harwood of CNBC and the New York Times that aired Tuesday, saying: “It’s a good issue to keep alive. . . . It’s fun to poke [Obama] a little bit and say, ‘Hey, let’s see your grades and your birth certificate.’ I don’t have a clue about where the president — and what this birth certificate says.”

Perry may have been trying to get under Obama’s skin and show Republicans that he would stand up to the president aggressively on any front. “I’m really not worried about the president’s birth certificate,” the governor told Harwood.

On Tuesday, Perry’s aides tried to turn attention away from the candidate’s comments. Asked to explain the strategy behind Perry’s fanning the birther rumors, campaign spokesman Mark Miner said: “It’s a non-issue. The governor is focused on improving the economy and creating jobs, issues Americans are truly concerned about.”

Still, Perry’s remarks alarmed some powerful Republicans, who quickly condemned his comments and said they distract voters from the one issue Republicans think they can ride to the White House: Obama’s record.

“If this election is about Barack Obama’s policies and the results of those policies, Barack Obama’s gonna lose,” Mississippi Gov. Haley Barbour told reporters Tuesday. “Any other issue that gets injected into the campaign is not good for the Republicans.”

Strategist Karl Rove, who has a well-documented rift with Perry, said on Fox News Channel: “You associate yourself with a nutty view like that and you damage yourself. . . . It starts to marginalize you in the minds of some of the people whom you need in order to get the election.”

Former Florida governor Jeb Bush wrote in a statement to Jennifer Rubin, a conservative opinion blogger at The Washington Post: “Republican candidates should categorically reject the notion that President Obama was not born in the United States. It is a complete distraction from the failed economic policies of the President.”

Some of Perry’s rivals had condemned such talk long ago; others do not appear to have broached the subject.

In April, with Trump pushing the birther issue, former Massachusetts governor Mitt Romney said Obama’s “citizenship test has been passed.”

“I believe the president was born in the United States,” Romney told CNBC’s Larry Kudlow. “There are real reasons to get this guy out of office. The man needs to be taken out of office, but his citizenship isn’t the reason why.”

Former Utah governor Jon Huntsman Jr. tweeted on Tuesday: “Barack Obama was born in America. Period. Let’s stop this and focus instead on how we fix the economy that he bungled.”

By Tuesday afternoon, Perry seemed to back away from his remarks. Asked at a news conference in Columbia, S.C., what it would take to convince him that Obama was born in the United States, he sidestepped the question, saying: “That is one of the biggest distractions that there is going.” When another reporter shouted, “Answer the question,” Perry did not.

“We need to be talking about jobs,” Perry added. “If somebody wants to see my birth certificate, I can show it to them. But the fact is that is a distraction and Americans really don’t care about that.”

Polling shows that a dwindling number of voters believe the birther theories. In an April 2010 Washington Post poll, about 1 in 3 Republicans said they thought Obama was born outside the United States. By April 2011, that number had dipped to 14 percent. It was far lower among independents and Democrats.

“It’s a moot issue,” said Saul Anuzis, a Romney backer and Republican National Committee member from Michigan. “You’re appealing to a small fringe group that does not add to the public discourse or the debate in this country. I’m dumbfounded.

In April, Obama released his birth certificate and denounced the persistence of conspiracy theories, saying the rumors had been fueled by “sideshows and carnival barkers.”

Asked why he thought Perry was bringing up the issue, former Obama spokesman Bill Burton, who runs a pro-Obama political action committee, said: “The man brought in the former head of federal disaster management to save his campaign. I don’t get the sense that there’s much strategy in what he’s doing here.”

Burton was referring to Joe Allbaugh, Perry’s new senior adviser.

Henry Barbour, a Perry fundraiser and adviser, who is also an RNC member from Mississippi and a nephew of Gov. Barbour, said Perry’s comments were “certainly off-message.”

“I think it was an undeliberate, unplanned act, in my opinion,” he said. “It might be fun, but I’m not sure it’s constructive.”

Staff writers Perry Bacon Jr. in Columbia, S.C., and Chris Cillizza in Washington contributed to this report.