MIAMI The Republican presidential rivals courted influential Hispanic voters in South Florida on Friday with promises to improve immigration laws and focus on Latin America, as a new poll suggested Mitt Romney is regaining his edge in the first mega-state to deliver a decision.

A survey by Connecticut-based Quinnipiac University - conducted less than a week before voters go to the polls - found Romney leading the once-surging Newt Gingrich by 38 percent to 29 percent in what's become a two-man race.

Romney and Gingrich appeared hours apart before a crowd at the center-right Hispanic Leadership Network, where Sen. Marco Rubio, R-Fla., preceded them onstage. They refrained from the attacks that have defined the campaign, though they continued to disagree on what to do with the estimated 11 million people who live in the U.S. illegally.

Without mentioning a Gingrich attack ad that the campaign withdrew after complaints from Rubio, Romney sought to defend himself from the ad's accusation that he was anti-immigrant.

"We are not anti-immigrant. We are not anti-immigration," said Romney, who called the suggestion "repulsive" Thursday night as he aggressively hit back at Gingrich during a debate. "We are the pro-immigration, pro-legality, pro-citizenship nation."

Front-runners talk immigration

Romney appeared to be riding a wave from his pull-no-punches debate performance, and he appeared relaxed and jovial Friday before the Hispanic group, which gave him several rounds of applause and a standing ovation when he pledged to "help Cuba become free."

He also said he'd appoint a presidential envoy responsible for democracy and freedom in Latin America.

He defended his call for those who are in the U.S. illegally to be given a temporary status and then return to their home countries to apply for citizenship.

"Other people call that self-deportation," he said, adding, "we're not going to go out and round up people in buses and send them home," he said.

Gingrich sought to draw a line of distinction, saying he had a "big disagreement with Gov. Romney." He said "a very significant number" of "young, unattached" undocumented immigrants would go back to their countries and apply for a guest-worker program under Romney's plan.

"Self-deportation in fact works for those groups," he admitted, but not for everyone. "The idea that a grandmother is not going to be supported, the idea that she's going to self-deport ... this is not a solution."

Santorum shares immigrant ties

Former Pennsylvania Sen. Rick Santorum, who picked up the endorsement of the Latin Builders Association, told the group the story of his grandfather, an Italian immigrant who worked in Pennsylvania coal mines until he was 72.

"Those were the hands that dug freedom for me in America," he said.

Santorum then vowed to take a hard line against any alliance between Iran and Venezuela, which he described as "Cuba Part B."