More than 600 suspected gang members have been arrested in the Homeland Security Department’s latest crackdown on street gangs, Immigration and Customs Enforcement officials said Thursday.

ICE agents, along with local authorities in 179 cities, arrested 638 suspected gang members over a monthlong period in March and April.

ICE officials said 78 suspected gang members were arrested on federal charges while another 447 currently face only state charges. ICE arrested 113 others on administrative immigration charges....