Elorza told CNN's Carol Costello that, regardless of any new policies, his city will "stand up for our undocumented immigrant families."
"People in the community, they are concerned and they are scared because of what they heard from Donald Trump during the campaign. And for me it's very important to reassure all our residents that, regardless of what they hear at the national level, they are safe here in Providence and we have their back," insisted Elorza.
Asked by Costello if this stance would change when it comes to undocumented immigrants who commit violent crimes, a scenario that Trump continually referenced during his presidential campaign
, Elorza said the rules were clear.
"If folks are committing crimes or if there's a criminal warrant, those folks, there's cooperation with the ICE [Immigration and Customs Enforcement], not just in Providence, but across the country" he said.
The people he would endeavor to protect, he told Costello, are those living "law-abiding lives."
"This isn't about folks who are committing crimes or violent crimes or have criminal detainers against them. This is about otherwise law-abiding folks, just going about their business. They are part of our community and mayors across the country are going to continue to stand up for them," Elorza said.
Despite Trump's campaign promises
to forcibly deport the estimated 11 million undocumented immigrants in the country, as well as to block federal funding to so-called "sanctuary-cities," Elorza said he was heartened by what he perceived as a softening by the President-elect on the issue.
"What has been encouraging up to this point is to hear that Donald Trump has walked away from his more concerning and frankly, terrifying rhetoric to go, sort of, house-by-house and door-to-door to find folks who don't have documented immigration status," he said.
Yet, regardless of any new federal laws on immigration that Trump may or may not put into place, Elorza said he would stand by the undocumented immigrants in his city, and that they should not be afraid
"Mayors across the country are standing up to speak for them because they are part of our community" he said,
"We will make sure they're safe," he added.