In a surprise announcement, the Obama administration said it will review the deportation cases of 300,000 illegal immigrants and might allow many of them to stay in the U.S., a decision that angered immigration hard-liners and pleased Hispanic advocacy groups.

Under the plan, federal authorities will review individually all cases of immigrants currently in deportation proceedings. Those who haven't committed crimes and who aren't considered a threat to public safety will have a chance to stay in the U.S. and to later apply...