The Iowa congressman says "maybe the best thing we could do for our neighbors to the South is give them back their talent and restore our rule of law."
King is opposed to a program under former President Barack Obama that granted a deportation reprieve to about 800,000 young immigrants.
President Donald Trump is phasing out the Deferred Action for Childhood Arrivals program, but gave Congress six months to act before recipients' work permits begin to expire.
House and Senate leaders say they want a legislative solution to extend protections, but prospects are uncertain.
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Republican Rep. Steve King says young immigrants brought to the United States as children and now here illegally would generate an economic lift for Mexico and other Central American nations if they were to return.