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(CNN) -- Rick Santorum finished the Iowa Republican caucuses 34 votes ahead of Mitt Romney, but results from several precincts are missing and the full actual results may never be known, according to a final certified tally released Thursday by the Iowa GOP.
The new numbers show 29,839 votes for Santorum and 29,805 votes for Romney, according to the party.
The initial returns from Iowa gave Romney a razor-thin eight-vote margin of victory over Santorum, reinforcing the former Massachusetts governor's frontrunner status and giving him a major momentum boost heading into the New Hampshire primaries.
Romney went on to win New Hampshire easily, seemingly making him the first non-incumbent Republican in modern history to win the first two contests of the cycle.
Now history is being rewritten, casting a shadow over the first-in-the-nation caucuses and potentially shaking up the GOP race two days before the critical South Carolina primary.
Santorum said on CNN's "The Situation Room with Wolf Blitzer" that the victory, while delayed, was sweet.
"We feel very, very good that we not only won, but that we .... pulled off a huge upset," the former Pennsylvania senator said in the interview to be broadcast later Thursday.
Romney called Santorum after the revised result came out, according to both campaigns. However, they differed on whether Romney called to concede, as claimed by Santorum spokesman Hogan Gidley.
A top Romney staffer disputed that any concession occurred, while campaign spokeswoman Andrea Saul said: "Gov. Romney called Sen. Santorum to congratulate him on the Iowa results."
In the CNN interview, Santorum said he got an e-mail before 5 a.m. Thursday informing him of his 34-vote victory in the certified results. He also said his margin of victory would be higher if uncertified results from other precincts were included.
"Either way you tally it, we were successful. And we feel very good about that," Santorum said, adding his campaign is working to "continue that momentum and take it here to South Carolina now and off to Florida."
Eventually, he said, the Republican presidential race will narrow to a lone conservative contender against the more moderate Romney. Asked if he was disappointed that the Iowa results took so long to certify, possibly denying him momentum in last week's New Hampshire primary, Santorum said: "I don't blame Iowa."
"If you think about it, it moved from eight votes to 34. Usually in an election, that kind of change is insignificant," he said.
Gidley earlier told CNN that the revised result was "exciting because the narrative for a long time has been that Mitt Romney was 2-0."
"That's not the narrative anymore," Gidley said. "There have been two states, two different victors."
Romney's eight-vote win was seen as "a huge victory," Gidley said. "By that standard, I guess 34 votes is just about a landslide in Iowa."
While Santorum had a slight advantage in the certified tally, results from eight precincts were missing and will never be recovered -- a fact that leaves the question of who actually finished first in the caucuses unanswered.
"I congratulate Sen. Santorum and Gov. Romney on a hard-fought effort during the closest contest in caucus history," Iowa GOP Chairman Matt Strawn said in a written statement. "Our goal throughout the certification process was to most accurately reflect and report how Iowans voted."
Romney said in a written statement Thursday morning that the new results show a "virtual tie" between the two candidates.
"The results from Iowa caucus night revealed a virtual tie," Romney said. "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."
"The Iowa caucuses, with record turnout, were a great start to defeating President Obama in Iowa and elsewhere in the general election," Romney added.
One week after Iowa's January 3 caucuses, Romney won the New Hampshire primary with nearly 40% of primary votes. In that contest, Santorum, a former Pennsylvania senator, finished in fifth place with 9%.
The South Carolina primary is scheduled for Saturday. The Palmetto State has picked the winner of every GOP nomination fight since 1980. Romney currently appears to be clinging to a dwindling lead there over former House Speaker Newt Gingrich.
A Republican debate will be held Thursday night in Charleston, South Carolina.
"The bottom line is, it's really going to make a boost to our campaign today and remind people just that we've been able to tackle and take on Mitt Romney head-on," Gidley said. "We are the alternative to him, and we plan on taking this into South Carolina and beyond and showing folks that we've got the message and the messenger that can beat the guy who's just writing checks, trying to buy a state."
Gidley said he can "understand how the Romney campaign is out there trying to marginalize the victory. I can understand he doesn't want that narrative out there, but it's a big win for our campaign and we're really excited about it."
CNN Chief Political Correspondent Candy Crowley said she doesn't believe the Iowa development will change the big picture for the prospective nominees.
"I think it does give Rick Santorum bragging rights," she said. "Any time you can grab the headlines, that's a good thing." But, she said, the results are not that different from the close margin seen just after the caucuses.
CNN's Dana Bash and Rachel Streitfeld contributed to this report.