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Washington CNN —  

Louisiana Gov. Bobby Jindal said Monday he would hold mayors of so-called sanctuary cities “criminally culpable” for crimes committed by undocumented immigrants in their cities.

Sanctuary cities like San Francisco often do not honor federal authorities’ requests to hold undocumented immigrants in custody so they can be deported – policies that have come under the microscope after an undocumented immigrant who had recently evaded deportation allegedly shot and killed 32-year-old Kate Steinle in San Francisco.

“Absolutely,” Jindal, who is a Republican contender for the presidency, said Monday morning on Boston Herald Radio when asked whether he believed mayors of those cities should be arrested. “I would hold them as an accomplice. Make them criminally culpable.”

Jindal added that he thinks those mayors should also be liable for civil damages.

“Especially if the prosecutor isn’t taking action or if the mayor’s not changing their ways, I’d allow the families to go to court and sue them civilly as well to recover damages,” Jindal said.

READ: Jindal won’t say how he’ll handle 11 million undocumented immigrants

The comments come after Jindal announced last Thursday a “partners in crime” plan to hold city officials accountable for the crimes of undocumented immigrants in their cities. The plan calls for Congress to pass legislation that would make city officials “an accessory” to those crimes and give victims’ families standing to sue.

Heading into the first Republican debate, Jindal has picked up the immigration baton as he looks to rise from the dredges of the latest polls and snag a spot amid the top 10 candidates who will debate in primetime Thursday.

The issue has helped galvanize supporters of the leader in Republican polls, Donald Trump, who has employed sharp rhetoric in addressing illegal immigration. Trump first drew attention to Steinle’s murder and brought attention to the issue of sanctuary cities.

Fellow GOP contender Jeb Bush, the former Florida governor who supports comprehensive immigration reform and a path to legal status for undocumented immigrants, also slammed sanctuary cities on Monday and said the federal government should withhold funds to those cities.

READ: How Jeb Bush would secure the border

Jindal’s policy platform on illegal immigration remains short on details though. Jindal has called for securing the border but refuses to say how he would deal with the more than 11 million undocumented immigrants living in the U.S.

Jindal is, though, happy to explain his plans for the mayors of sanctuary cities, insisting that the policies – which are intended to reassure undocumented immigrants that they or their loved ones won’t be deported for reporting a crime or calling the police – must be criminalized and city officials held accountable.

“One of the things we can and should be doing right now is cracking down on the sanctuary cities,” Jindal said Monday. “It makes no sense for these mayors, these local politicians, to be able to ignore the law (and) choose which ones they want to enforce.”

READ: Immigrants and crime: Crunching the numbers