The top-tier Republican presidential candidates escalated their long-running spat over illegal immigration Tuesday during campaign stops in the Midwest, a day after frontrunner Rudy Giuliani opened himself to attacks by saying his permissive immigration policies while mayor of New York City helped reduce crime.

Illegal immigration has emerged as a defining issue in the GOP race, as the candidates continue to accuse each other of backing liberal immigration policies.

"I think the discussion over illegal immigration says something about where you come from, your conservative perspective on the rule of law," former Massachusetts Gov. Mitt Romney said after talking about health care in Des Moines, Iowa.

And he responded sharply to Giuliani's statements along the Texas-Mexico border Monday that by not strictly enforcing illegal immigration laws in New York, he lowered crime.

"I was surprised yesterday to see that Mayor Giuliani, instead of distancing himself from his sanctuary policies as mayor, said that the sanctuary illegal alien policies he had as mayor made his city more lawful, orderly and legal ... that is turning reason on its head," Romney said.

Giuliani said Monday that his policies "were in the context of overall policies that probably were the most successful in the history of the country in creating an orderly, legal, lawful society."

Giuliani has said that he discouraged rounding up illegal immigrants so they would feel free to report crime, contributing to the city's safety improvement.

Though Romney has accused Giuliani of presiding over a so-called sanctuary city, there were at least five similar cities with similar policies in Massachusetts while Romney was governor.

But there was another potential "sanctuary city" on the list of talking points Tuesday, as the Des Moines Register reported that the Des Moines City Council could consider a proposal to prevent law enforcement officials from conducting raids on illegal immigrants in the city.

GOP candidate Fred Thompson used the news to take another swipe at his opponents.

"I don't believe at the end of the day Des Moines wants to follow the pattern of New York City or Little Rock, Arkansas. I think they will reject becoming a sanctuary city or anything close to that," he said.

The Little Rock comment was aimed squarely at former Arkansas Gov. Mike Huckabee, who has said he favors allowing illegal immigrants already in the U.S. to earn legal status, and who proposed state services for them while he was governor.

Huckabee has attracted fire from his opponents as he rises in the polls. Several recent Iowa polls have shown Huckabee coming from behind and scooting into second place in the early-voting state. An American Research Group poll taken Nov. 10-14 of 600 likely voters showed Huckabee with 24 percent support, behind Romney with 26 percent. The poll had Thompson and Giuliani tied at 11 percent. The margin of error was 4 points.

FOX News' Carl Cameron and The Associated Press contributed to this report.