CONCORD, N.H. – Presidential hopeful Mitt Romney criticizes “sanctuary cities” for illegal immigrants – and by implication Republican rival Rudy Giuliani – in a new radio ad.

“Immigration laws don’t work if they’re ignored. That’s the problem with cities like Newark, San Francisco and New York City that adopt sanctuary policies,” an announcer says in the ad, which runs in New Hampshire and Iowa. “Sanctuary cities become magnets that encourage illegal immigration and undermine secure borders.”

Romney and Giuliani have jabbed over immigration in recent weeks. The former Massachusetts governor says Giuliani promoted New York as a haven for illegal immigrants when he was mayor. Giuliani aggressively denies it, insisting he cracked down on lawlessness of every kind.

“Legal immigration is great,” Romney says in the new ad. “But illegal immigration, that we’ve got to end. And amnesty is not the way to do it.”

In so-called sanctuary cities, government employees are not required to report illegal immigrants to federal authorities. Some, such as San Francisco, have declared themselves sanctuaries or refuges. Others, like New York, have never adopted the name.

New York’s policy, begun by Democratic Mayor Ed Koch in 1988, is intended to make immigrants feel that they can report crimes, send their children to school or seek medical treatment without fear of being reported. An estimated half million illegal immigrants live in New York.

Romney has pledged to cut federal funds from cities that adopt “sanctuary policies” and ignore federal immigration laws.

Last week, Giuliani began running a radio ad that highlights his support for building a fence along the U.S.-Mexican border. He says that as mayor he unsuccessfully tried to get federal help to deport illegal immigrants convicted of crimes. He also tells voters that as president he would require new immigrants to learn English, deport criminal suspects and enact tougher visa standards.