Rick Santorum’s campaign claimed a belated victory in the Iowa caucuses on Thursday morning after certified results from the contest showed him leading Mitt Romney by 34 votes, a reversal from the eight-vote edge for Mr. Romney on caucus night.

Matt Strawn, chairman of Iowa’s Republican Party, announced Thursday morning that an actual winner could not be determined in the caucuses because results from eight of 1,774 precincts could not be located for certification. But of the votes that could be reviewed by the party, the officials said, Mr. Santorum finished narrowly ahead of Mr. Romney.

“Just as I did in the early morning hours on Jan. 4, I congratulate Senator Santorum and Governor Romney on a hard-fought effort during the closest contest in caucus history,” Mr. Strawn said in a statement. “Our goal throughout the certification process was to most accurately reflect and report how Iowans voted the evening of Jan. 3. We understand the importance to the candidates involved, but as Iowans, we understand the responsibility we have as temporary caretakers of the Iowa caucuses.”

The certified results found that Mr. Santorum received 29,839 votes, and Mr. Romney received 29,805 votes.

Mr. Romney called Mr. Santorum on Thursday to concede the Iowa caucuses, a spokesman for Mr. Santorum said. The call affirmed the Santorum victory in Iowa.

In a Twitter message to his supporters Thursday morning, Mr. Santorum wrote: “Thank you Iowa for the win! I encourage everyone to join our fight in South Carolina! Game on!”

He will argue to voters in South Carolina, aides said, that the result shows that he is the best-equipped candidate to emerge as a conservative alternative to Mr. Romney.

“The history books will read that the winner of the Iowa caucuses in 2012 is Rick Santorum. That’s the bottom line,” Hogan Gidley, an adviser to Mr. Santorum said in an interview Thursday. “This just goes to prove what we’ve been saying: We can take it right to Mitt Romney with a fraction of the resources and beat him. We can do the same to Barack Obama.”

Mr. Romney’s campaign shrugged off the new vote totals, saying that it had always considered the Iowa results to have been a virtual tie.

“The results from Iowa caucus night revealed a virtual tie,” Mr. Romney said in an e-mail statement to reporters. “I would like to thank the Iowa Republican Party for their careful attention to the caucus process, and we once again recognize Rick Santorum for his strong performance in the state.”

Two party officials in the state, speaking on condition of anonymity, said the decision to avoid naming an official winner was not made to avoid embarrassing Mr. Romney, who is moving closer to the Republican nomination, but rather was the only option after a thorough review of the votes that could be located.

That ruling, first reported by The Des Moines Register, has no practical effect — the Iowa contest is considered a “beauty contest” that does not officially allocate delegates to the winner, but provides Iowa’s Republican Party a sense of the voters’ thinking.

But the muddled result could be a psychological gain for Mr. Santorum, and robs Mr. Romney of being able to say that he swept the early contests.

And it comes as the men are battling in South Carolina, which holds its primary Saturday. Mr. Romney, in particular, has hit one of the roughest patches of his second bid for the White House as he struggles with concerns about his personal wealth and his taxes.

In his statement, Mr. Romney kept his focus on the battle ahead should he win the nomination.

“The Iowa caucuses, with record turnout, were a great start to defeating President Obama in Iowa and elsewhere in the general election,” he said.

Mr. Santorum, too, had initially referred to the results in Iowa as a tie. He told Fox News shortly after the caucuses ended that he dismissed reports about possible errors in the count.

“That doesn’t really matter to me. I mean, this was a tie,” Mr. Santorum said on the network at the time.