Former senator Rick Santorum (Pa.) pulled out narrow wins in the Alabama and Mississippi presidential primaries Tuesday, bolstering his claim to being the conservative alternative to Republican front-runner Mitt Romney.

“We did it again,” Santorum told cheering supporters in Lafayette, La.; that state will hold its primary March 24. “Who would have thought . . . that ordinary folks from across this country can defy the odds day in and day out?”

Santorum had been heavily outspent by Romney and did not have anything close to the front-runner’s superior organization.

“The time is now for conservatives to pull together,” Santorum said, adding that “the best chance to win this election is to nominate a conservative to go up against Barack Obama who can take him on on every issue.”

Romney had put an aggressive, late-hour effort into a part of the country that was considered hostile territory for him — one where a win seemed almost inconceivable only a few weeks ago.

Romney won the two smaller contests of the day: the caucuses in Hawaii and American Samoa, where he picked up all six delagates and three superdelegates. Romney won 45 percent of the vote in Hawaii, followed by Santorum with 25 percent and Ron Paul with 18. Gingrich came fourth with 11 percent.

The former Massachusetts governor had played down his expectations in the South. But in an interview on Tuesday with CNN, he spoke dismissively of his closest competitor.

“Senator Santorum is at the desperate end of his campaign,” Romney said.

Santorum and former House speaker Newt Gingrich (Ga.) have both laid claim to the conservative mantle. But without a win Tuesday in what is essentially his home region, Gingrich may find it difficult to marshal the resources — and a rationale — to continue his campaign.

Gingrich gave no indication Tuesday night that he would end his bid, and he grasped for a silver lining in the fact that Romney also fell short.

“The elite media’s effort to convince the nation that Mitt Romney is inevitable just collapsed,” Gingrich said at a rally in Birmingham, Ala. “If you’re a front-runner and you keep coming in third, you’re not much of a front-runner.”

In both states, Rep. Ron Paul (Tex.) ran far behind the three leading contenders.

With Santorum and Gingrich remaining in the race, Romney has been able to exploit the split they have created among the most conservative Republicans, and to build a slow but steady lead in the contest for convention delegates.

Going into Tuesday’s primaries, Romney had 438 delegates, about twice as many as Santorum, who was in second place.

“He’s far behind in the delegate count; he’s far behind in the popular-vote count,” Romney said of the former senator, adding: “If you look at the math . . . it’s a very difficult road for him.”

Romney himself remains well short of the 1,144 delegates it will take to clinch the nomination.

At this point, it is almost mathematically impossible for any of Romney’s rivals to reach that goal, but they are holding on to the hope that by denying him the number he needs, they can take the fight into August and to the Republican National Convention in Tampa.

The stakes on Tuesday were perhaps highest for Gingrich, who has the best claim to being a Southerner: He spent part of his childhood in Georgia and represented the Atlanta area for decades in Congress. He has won only two primaries, in Georgia and South Carolina, and is falling further behind the two leading contenders.

“This is pretty important,” said Rick Tyler, a longtime Gingrich aide who is now running a super PAC that has poured millions of independent expenditures into supporting the former speaker’s candidacy. “The PAC always felt we needed to win both of these states to change the narrative.”

In Mississippi in particular, Romney struggled to prove that he could make a strong showing in an electorate dominated by the GOP factions that have been the most hostile toward his candidacy.

At least eight in 10 voters in Mississippi and Alabama identified themselves in exit polls as evangelical Christians, a group that has been suspicious of Romney’s Mormon faith and of his past support for abortion rights.

Typically, Republicans anoint their nominee early. But this year has produced the most unpredictable and bitter fight in recent history, one that is pitting the establishment wing of the GOP against the insurgent forces of the tea party and social conservatives.

The races in Mississippi and Alabama picked up intensity after the mixed results of the March 6 Super Tuesday contests, which did not winnow the field as many had expected.

“Most people would have said a month ago it will be over by the time you get to Mississippi and Alabama,” said former senator Trent Lott (R-Miss.), a Romney supporter.

Romney’s supporters had hoped that he could put to rest questions about whether he can win over the party’s base.

Exit polls Tuesday suggested that electability was the foremost concern of voters in the two Southern states, as it had been in many of the earlier primaries. A plurality in both Mississippi and Alabama said the quality that mattered most to them in deciding which candidate to support was whether he can beat Obama.

But Santorum triumphed because just as many voters said that having a “strong moral character” or being a “true conservative” were the most important attributes. He won these voters by big margins.

Some Romney supporters suggested that Republican voters may be growing anxious to see this prolonged nominating contest come to an end, so that the nominee can begin marshaling an organization and financial support for the general-election contest.

“As the race progresses, the drumbeat gets louder and louder to get it over,” said Romney supporter Henry Barbour, a nephew of former Mississippi governor Haley Barbour and a Republican national committeeman.

Romney benefited from the muscle of the Mississippi political establishment. Nearly every Republican official elected statewide lined up behind him, including Gov. Phil Bryant, who gave Romney a late endorsement last week after initially backing the candidacy of Texas Gov. Rick Perry.

Henry Barbour’s younger brother Austin ran much of the Romney campaign’s ground operation in the state, and state auditor Stacey Pickering, who also has a surname famous in Mississippi Republican politics, was chairman of Romney’s campaign there.

Staff researcher Lucy Shackelford and polling manager Peyton Craighill contributed to this report.