Not to be outdone by his Republican presidential rivals on immigration, Gov. Bobby Jindal of Louisiana said Friday that he could secure the Southern border within six months of becoming president and called for prosecuting officials in sanctuary cities when their undocumented residents commit crimes.

“A smart immigration policy will make our country stronger — a dumb immigration policy will make it weaker,” Mr. Jindal said at a Defending the American Dream Summit hosted by Americans for Prosperity in Columbus, Ohio. “Today, we have a dumb immigration policy.”

Republicans have been ramping up their stance on immigration since Donald J. Trump surged in the polls after taking a hard line on the issue and vowing to build a wall to prevent people from other countries from sneaking in.