Philadelphia remains a "sanctuary city" despite a threat to its future status from President-elect Donald Trump, Mayor Kenney said Thursday.

Sanctuary cities do not cooperate with federal immigration officials in holding undocumented immigrants in custody for nonviolent crimes. Trump has threatened to withhold federal funds from cities that adopt the practice.

Kenney restored Philadelphia's sanctuary status when he took office and defended the policy Thursday, with a little rebranding.

"First of all, we've changed the name from 'sanctuary city' to 'the Fourth Amendment city,' " Kenney said. "We respect and live up to the Fourth Amendment, which means you can't be held against your will without a warrant from the court signed by a judge. So, yeah, we will continue to be a Fourth Amendment city abiding by the Constitution."

Kenney did not want to speculate on what he would do should Trump follow through on his promise to strip Philadelphia and cities like it of millions of dollars in federal money.

"We'll cross that bridge when we come to it, and we'll see how it goes and we'll try to figure something out," Kenney said.

Kenney said he thinks the Constitution's protection against unlawful search and seizure is on his side.

"We have no authority to violate the Fourth Amendment. All the immigration officials have to do is get a warrant signed by a federal magistrate and we'll be happy to turn that person over," he said.

The policy blocks police from complying with Immigration and Customs Enforcement detainer requests or from notifying federal officials when a prisoner who is undocumented is being released - unless that person has been convicted of a violent felony and federal agents have obtained a warrant.

Advocates say it improves immigrant-police relations and encourages undocumented people who need help to seek it without threat of deportation. Critics say it's a threat to safety and security.

In July, the U.S. Justice Department said it would withhold some law enforcement grant money from cities that do not comply. The issue became a key dispute in the Senate race between U.S. Sen. Pat Toomey (R., Pa.) and his defeated challenger, Katie McGinty.

On Thursday, Kenney also commented on the anti-Trump rallies and instances of graffiti - both pro and anti-Trump - citywide.

"Take a breath," Kenney said. "It was a very divisive election, a difficult election, but again, it's over, and we have to move forward as a country."