8:48 p.m. ET Jan. 25, 2017   Several big city mayors across the U.S. vowed on Wednesday to defy President Trump’s executive order that threatens to cut off federal funding to cities that offer some sort of protection to undocumented immigrants in their communities.

The pushback from the mayors came as Trump signed a long-anticipated executive order that directs the government to identify federal money it can withhold to punish so-called "sanctuary cities," a term for hundreds of communities that in some way limit cooperation with federal immigration enforcement agents. Trump had pledged to take action against sanctuary cities on the campaign trail.

But as Trump announced the order — as well as action to build a wall along the U.S-Mexico border and hire thousands of new border patrol agents and immigration officers — leaders of some of the nation's biggest cities flatly stated they would not be cooperating with the president.

In New York, Mayor Bill de Blasio vowed that the action “won’t change how we enforce the law in New York City.”

De Blasio said that the city has been able to dramatically reduce the crime rate in the nation’s largest city, in part, because relationships the police department has managed to build in immigrant communities. He added that if Trump went through with his plan to slash funds it would lead to the president, a native New Yorker, cutting funding from the New York Police Department. An early analysis by NYC officials suggested that about $156 million in federal funding for the NYPD could be impacted.

“Here in New York City and in cities across the nation, this executive order could in fact undermine public safety and make our neighborhoods less safe,” De Blasio said.

In Boston, Mayor Marty Walsh called the executive order an attack on "Boston’s people, Boston’s strength and Boston’s values.”

“If people want to live here, they’ll live here,” Walsh told reporters at a news conference. “They can use my office. They can use any office in this building.”

In Seattle, Mayor Ed Murray said that he had directed city departments to review their budgets to prepare for a potential loss of federal funding, the Associated Press reports.

"This city will not be bullied by this administration," Murray said. "We believe we have the rule of law and the courts on our side."

In Chicago, where Trump has pilloried the mayor over the surge in violence in the city, Mayor Rahm Emanuel vowed that the nation’s third largest city would remain a sanctuary city. Emanuel sidestepped questions at an afternoon news conference about how the city would weather a potential cut in federal funding.

“I want to be clear. We're gonna stay a sanctuary city," Emanuel said. "There is no stranger among us. We welcome people, whether you're from Poland or Pakistan, whether you're from Ireland or India or Israel and whether you're from Mexico or Moldova, where my grandfather came from, you are welcome in Chicago as you pursue the American Dream."

In San Francisco, Mayor Ed Lee told reporters after Trump signed the executive order that nothing has changed for his city.

“I am here today to say we are still a sanctuary city,” Lee said. “We stand by our sanctuary city because we want everybody to feel safe and utilize the services they deserve, including education and health care.”

Both Lee and De Blasio said that early readings of the executive order by their cities' attorneys suggest that the document is vaguely written and predicted that the Trump administration would face a tough legal battle if it tries to use it as a basis to slash funding.

“There is less here than meets the eye,” De Blasio said of the order.

In Detroit, a top aide to Mayor Mike Duggan, questioned whether the city even qualified as a sanctuary city.

The Detroit City Council in 2007 passed legislation prohibiting city employees, including police, form asking about person’s immigration status unless it was directly related to an alleged crime. City officials say that Detroit police, however, regularly cooperated with requests from federal immigration officials.

“We do not believe this applies to the city of Detroit," said Alexis Wiley, Mayor Mike Duggan's chief of staff. "We do cooperate fully with all federal agencies during the course of criminal investigations, regardless of a person’s immigration status.”

The U.S. Conference of Mayors and the Major Cities Chief Association expressed concern that the executive order is overly vague.

“That order does not provide a clear definition of what constitutes a sanctuary jurisdiction,” the organizations said in a joint statement. “Instead, it gives undefined discretion to the Secretary of Homeland Security to designate sanctuary jurisdictions and the Attorney General to take action against them. We call upon the Secretary of Homeland Security to document and promulgate a lawful definition before further actions are taken, so the cities across the Nation may determine how to proceed."