WASHINGTON (Reuters) - Republican presidential candidate Rick Perry said on Wednesday he was wrong to say that opponents of his immigration policy in Texas have no heart, as he sought to dampen conservative ire over the comment.

Perry, the Texas governor, has drawn fire from rival candidates Mitt Romney and Michele Bachmann over remarks he used to defend a measure that allows children of illegal immigrants to pay cheaper in-state tuition rates at Texas colleges.

The policy is outside usual conservative orthodoxy and Perry compounded the issue by saying at a Florida debate last week to those who oppose it, "I don't think you have a heart."

"I probably chose a poor word to explain that to people who don't want their state to be giving tuition to illegal aliens, illegal immigrants in this country," Perry told Newsmax.TV in an interview.

"That's their call and I respect that," Perry said. "And I was probably a bit over-passionate by using that word and it was inappropriate. But here's what I do believe: It is a state's sovereign right to decide that for themselves. In Texas in 2001, we had 181 members of the legislature -- only four voted against this piece of legislation -- because it wasn't about immigration. It was about education."

Perry's comments suggested his campaign recognized the comment presented a problem for him within the conservative base, which has a hardline stance against illegal immigration.

The Romney campaign has pounced on the issue to try to raise doubts about him among conservatives.

"I think if you're opposed to illegal immigration, it doesn't mean that you don't have a heart. It means that you have a heart and a brain," Romney said last Friday.

Another Perry rival, businessman Herman Cain, told CNN on Wednesday he could not support Perry as the Republican presidential nominee for 2012, in part because of his immigration policy.

"Him being soft on securing the border is one of the reasons. I feel very strongly about the need to secure the border for real, the need to enforce the laws that are already there," he said.

Perry's remains the Republican front-runner despite a rocky debate performance. A CNN poll this week said he received 30 percent support, compared to Romney at 22 percent, Newt Gingrich at 11 percent, Herman Cain at 9 percent, Ron Paul at 7 percent and Michele Bachmann 6 percent.