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But the Republican says violence has caused "chaos" in Mexico, and the U.S. should not ignore people coming illegally from that "very violent atmosphere."
Bryant spoke Wednesday at a Capitol news conference hosted by the Mississippi Federation for Immigration Reform and Enforcement and the Mississippi Tea Party.
An immigration enforcement proposal, House Bill 488, awaits consideration in the House Education Committee.
Two Catholic bishops in Mississippi say they're concerned immigrant families could be hurt by the bill. Bishop Roger Morin of the Biloxi diocese says immigration is best handled by the federal government.