DES MOINES, Iowa (AP) - Rick Santorum and Mitt Romney waged a seesaw battle for supremacy in Iowa's Republican presidential caucuses late Tuesday night, the opening round of a campaign to pick a challenger to President Barack Obama.

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Texas Rep. Ron Paul ran third.

Returns from 93 percent of the state's 1,774 precincts showed Santorum, a former Pennsylvania senator, and Romney, a former governor of Massachusetts, in a near dead heat, a fitting conclusion to a race as jumbled as any since Iowa gained the lead-off position in presidential campaigns four decades ago.

Regardless of the outcome, there was enough for either man to claim a victory - Romney as the man to beat for the party's nomination and Santorum the leader among those struggling to emerge as his unvarnished conservative rival in the primaries yet to come.

New Hampshire votes next, and Romney is heavily favored in the first-in-the-nation primary on Jan. 10. South Carolina on Jan. 21 figures to be a tougher test, the first contest in a Southern state and one that is part of the Republican base.

Former House Speaker Newt Gingrich was headed for a fourth-place finish, trailed by Texas Gov. Rick Perry.

Minnesota Rep. Michele Bachmann was far behind, and her campaign manager, Keith Nahigian, suggested she might drop out.

Asked in an interview if he could say with certainty she would go forward with her candidacy, he told The Associated Press: "I don't know yet."

"It's hard to tell, but everything is planned," he added.

No matter how close the final results in Iowa, there were no plans for a recount.

Doug Heye, a spokesman for the state party, said the ballots were counted under the supervision of campaign representatives who certified the totals. He said the numbers were double-checked when they were reported to state officials and there was no reason to check them again.

"On to New Hampshire," Gingrich said to the cheers of his supporters, vowing to carry on his campaign no matter the Iowa outcome.

The former speaker led in the pre-caucus polls as recently as a few weeks ago, only to fall under the weight of attack ads run by a super PAC run by allies of Romney.