SAN JUAN, Puerto Rico — Mitt Romney scored an overwhelming win Sunday in Puerto Rico’s Republican presidential primary, trouncing chief rival Rick Santorum on the Caribbean island even as the two rivals looked ahead to more competitive contests this week in Illinois and Louisiana.
The victory in the US territory was so convincing that Romney, the GOP front-runner, won all 20 delegates to the national convention at stake because he got more than 50 percent of the vote. That padded his comfortable lead over Santorum in the race to amass 1,144 delegates to clinch the nomination.
Nevertheless, the GOP nomination fight is unlikely to end anytime soon, with Santorum refusing to step aside even though Romney is pulling further ahead in the delegate hunt.
As the day began, Santorum claimed he was in contest for the long haul because Romney is a weak front-runner.
‘‘This is a primary process where somebody had a huge advantage, huge money advantage, huge advantage of establishment support and he hasn’t been able to close the deal and even come close to closing the deal,’’ Santorum said. ‘‘That tells you that there’s a real flaw there.’’
Yet, Santorum sidestepped when asked if he would fight Romney on the convention floor if he failed before August to stop the former Massachusetts governor from getting the required number of delegates.
Romney, in turn, expressed confidence that he'd prevail.
‘‘I can’t tell you exactly how the process is going to work,’’ Romney said. ‘‘But I bet I'm going to become the nominee.’’
Both campaigned in Puerto Rico last week — in a campaign focused on statehood for the US territory — but Romney cut short his trip so he could head to Illinois and Santorum spent Sunday in Louisiana.
Illinois, a more moderate Midwestern state, votes Tuesday and is seen as more friendly territory for Romney, while Santorum is the favorite in the more conservative Southern state of Louisiana, which votes Saturday.
After the Puerto Rico victory, Romney had 521 delegates in his camp and Santorum had 253, according to The Associated Press’ tally. Former House Speaker Newt Gingrich trailed with 136 delegates and Texas Rep. Ron Paul had 50.
Enrique Melendez, the Republican representative on the Puerto Rican State Electoral Commission, told the AP that Romney ‘‘won the Puerto Rican primary by a huge margin and we are granting him the 20 delegates.’’
At this rate, Romney is on pace to capture the nomination in June unless Santorum or Gingrich is able to win decisively in the coming contests.
Both have said they would stay in the race and perhaps force the nomination to a fight at the GOP’s convention in Tampa if Romney doesn’t amass enough delegates to arrive with a mandate. That would turn the convention into an intra-party brawl for the first time since 1976.
Even as Santorum declined to commit to forcing a brokered convention, his advisers were working behind the scenes on a plan to persuade convention delegates to switch candidates if the former Pennsylvania senator fails to derail Romney before that.
Romney’s aides call this a fantasy scenario even as they try to prevent delegates from defecting.
Half of the states have yet to weigh in on a race with seemingly no end in sight anytime soon. That’s prompted fresh speculation within the GOP over whether a contested convention is likely.
Republican National Chairman Reince Priebus insisted that party will have a nominee sooner rather than later.
‘‘We’re only at halftime,’’ Priebus said. ‘‘I think that this process is going to play itself out. We will have a nominee, I think, fairly soon — one, two months away.’’
In Puerto Rico, the race was focused on the issue of statehood, and Melendez said, ‘‘This proves Gov. Romney’s electability and his ability to reach out to Hispanics and minorities.’’
Whether that’s true or not, Romney told Puerto Ricans he would support statehood while Santorum said English would have to be the official language of the island if it were to join the United States — a statement that roiled residents.
‘‘In Puerto Rico, we get along fine with both languages,’’ said Francisco Rodriguez, a 76-year-old architect who supported Romney and hopes Puerto Rico becomes the nation’s 51st state.
Even as Puerto Rico voted, Romney and Santorum traded barbs from afar.
‘‘Sen. Santorum has the same economic lightweight background the president has,’’ Romney told a crowd in Moline, Ill. He went a step further in Rockford, Ill., saying, ‘‘We’re not going to replace an economic lightweight with another economic lightweight.’’
That drew a Santorum retort: ‘‘If Mitt Romney’s an economic heavyweight, we’re in trouble.’’
Aside from a pair of TV interviews, Santorum spent the day visiting a pair of churches in Louisiana, sharing how his faith has shaped his political career and his opposition to abortion rights and gay marriage. He didn’t mention Romney or any of his other Republican opponents during talks at both churches.
He made clear he didn’t plan to exit the race anytime soon, saying in Bossier City, La., ‘‘One of the great blessings I've had in every political campaign is people underestimate me, people underestimate what God can do.’’
Yet, he was curt when asked about his odds in Illinois.
‘‘Keep working,’’ Santorum said after services there. ‘‘That’s all we can do.’
’Santorum spoke with CNN’s ‘‘State of the Union’’ and ABC’s ‘‘This Week.’’ Romney appeared on ‘‘Fox News Sunday,’’ and Priebus was interviewed on CBS’ ‘‘Face the Nation.’’
Elliott reported from Washington. Associated Press writers Andrew DeMillo in Bossier City, La., Steve Peoples in Moline, Ill., and Kasie Hunt in San Juan, Puerto Rico, contributed to this report.