ORLANDO, Fla. — Former Massachusetts Gov. Mitt Romney pressed his attack Friday on conservative concerns over presidential rival Rick Perry’s support of favorable tuition rates for some children of illegal immigrants, hitting the three-term Texas governor’s claim that critics of the law are simply heartless.

“I think if you are opposed to illegal immigration, it doesn’t mean that you don’t have a heart,” the former Massachusetts told a gathering here for a Conservative Political Action Conference. “It means that you have a heart and a brain.”

Mr. Romney again called for a fence along the southern border with Mexico to staunch the flow of illegal immigrants, additional troops and law enforcement personnel along the border, and for ending the “magnet” that draws illegal immigrants here — the employers who hire illegal immigrants and the states, such as Texas, that offer taxpayer-funded benefits for people who are here illegally.

“One of the things I still can’t get over is the idea that a state would give a $100,000 discount to illegals to go to school in their state,” he said, suggesting the subsidy carries an annual price of $22,000 per student. “It is simply wrong to create that kind of magnet. It cannot be sustained.”

The attack came just hours after the third Republican debate in as many weeks, where nine candidates squared off. Mr. Perry, who leads the GOP polls nationally and here in Florida, again found himself the main object of attack onstage, coming under repeated fire from his rivals, particularly over the Texas policy that allows illegal immigrants to receive in-state tuition rates at public colleges and universities...