Puerto Rico's residents cannot vote in general elections, but are set to award 20 delegates in their Sunday Republican primary.
Meanwhile, Romney was hoping to cement his lead in Illinois ahead of Tuesday's primary, with chief rival Santorum in Louisiana ahead of that state's vote on March 24.
Both Santorum and Romney weighed in on Afghanistan as the campaign briefly moved to the Sunday morning talk shows.
Romney said that President Barack Obama has failed in Afghanistan, and he blamed the president for the chaos there. Romney told "Fox News Sunday" that the president should have been "more engaged" with military commanders and Afghan President Hamid Karzai.
The former Massachusetts governor has emerged as the only Republican candidate not to question the U.S. commitment in Afghanistan, even as polls show that most Americans want to end it.
On ABC's "This Week" that Santorum said the U.S. should commit to "winning" in the region or get out, echoing comments rival Newt Gingrich made last week.
The former Massachusetts governor and former Pennsylvania senator both campaigned in Puerto Rico ahead of the voting.
But Romney dramatically curtailed his trip to the U.S. territory Saturday in favor of spending more time in Illinois, where polls have shown him slightly ahead of Santorum.
At issue in Puerto Rico's primary is the island's political status - statehood, independence or no change. Puerto Ricans will vote on that in November.
Romney has support from much of the establishment here, including Puerto Rican Gov. Luis Fortuno, who supports making the island the 51st state. Romney is confident about his prospects for winning many of the island's delegates.
Santorum has said he would support statehood if the November vote were decisive. He also has spent days explaining his comment that English would have to become the island's main language for Puerto Rico to realize statehood. Only a fraction of Puerto Rico's residents speak English fluently.
Puerto Rico's delegates will be split proportionally among the candidates, though if someone wins more than 50 percent of the vote they'll sweep them all.