WASHINGTON — One of President Trump’s most controversial initiatives is a pledge to deny federal funds to “sanctuary cities’’ such as Boston, Somerville, and Cambridge that refuse to obey his strict detention and deportation plans for undocumented immigrants. But a closer look suggests that such a move may not be legal.

The Globe interviewed several immigration law experts to explain the questionable nature and potential impact of Trump’s proposal.

What are sanctuary cities?

In the broad sense, sanctuary cities are municipalities where local governments have decided against actively aiding federal immigration authorities. In some such cities, police are instructed not to inquire about a resident’s immigration status or not to relay a person’s immigration status to federal authorities.

Exceptions can be made, in Boston and elsewhere, when the immigrant in question has an outstanding criminal warrant for a serious offense, the lawyers said.

But Boston Mayor Martin J. Walsh, Somerville Mayor Joseph Curtatone, and others argue that sanctuary city policies foster trust between undocumented residents and local law enforcement. Officials also say this policy conserves limited city resources for public safety, which is a priority of the federal government.

Susan Church, head of the New England chapter of the American Immigration Lawyers Association, said it’s important to remember that each city operates under its own set of rules, and that “sanctuary cities’’ is a political, not a legal, term. “If you look at Newton versus Boston versus Somerville, it’s different proposals and lists different things that police officers can and can’t do,’’ Church said.

What has Trump said and done about sanctuary cities?

Trump has frequently called the legality and purpose of sanctuary cities into question, as have his predecessors, including Barack Obama.

On Wednesday — in an executive order called “Enhancing Public Safety in the Interior of the United States’’ — Trump asserted that any city that flouts federal immigration enforcement requirements would not be “eligible to receive federal grants, except as deemed necessary for law enforcement purposes by the attorney general or the secretary.’’

Boston is projected to receive about $500 million in federal funds to boost public housing, schools, and other city departments in the 2017 fiscal year, according to the mayor’s office.

Republicans have previously suggested stripping sanctuary cities of federal funds, but the idea has never had such fervent support from the White House. Trump made opposition to illegal immigration a central part of his presidential campaign.

Would stripping funds from cities like Boston be legal?

Probably not, according to legal experts, the state attorney general’s office, and the office of Republican Governor Charlie Baker.

Church, the lawyer, cited several cases in which conservative judges ruled that the federal government could not coerce local policy by manipulating separately allocated funds.

“It appears to me, based on my review from case law, that there are severe limits on the federal government’s ability to control state and local entities by controlling the purse strings,’’ Church said. “There are some [exceptions], but when you get to the nitty-gritty of holding funds from cities and towns, it is always limited.’’

Eliana C. Nader, an immigration lawyer in Boston, said she thought it was unlikely that Trump could turn his hard-line rhetoric into action, because the sanctuary policy is so entrenched in many cities. But if Trump did succeed in denying federal funds, Nader said, the action would be legally murky, at best.

“I would need to know how they’re planning to do that before I can say either way,’’ Nader said.

Trump’s aides have not provided any legal rationale for withholding funding, and his spokesman did not respond to a request for comment on it.

In previous statements, Walsh has denounced Trump’s promise, and said that he believes it is the role of Congress to manage how the federal government allocates its money.

Massachusetts Attorney General Maura Healey, a Democrat, also released a statement that said she found Trump’s proposed action to be illegal.

“The president’s executive order is an irresponsible attempt to coerce our communities into conducting his mass deportations,’’ she said.

A spokeswoman for Baker said the governor also believes that municipalities should be allowed to make their own decisions about cooperating with federal immigration authorities.

However, Baker opposes making Massachusetts a “sanctuary state.’’

“The administration will continue to enforce policies giving the State Police the tools necessary to detain violent criminals or suspected terrorists,’’ said Lizzy Guyton, Baker’s communications director.

So what’s going to happen?

The future is unclear, the lawyers said.

If Trump succeeds in stripping away funding from cities — a big if, legally speaking — cities could amend their policies to be in compliance, or choose to file lawsuits.

“It’s very complicated,’’ Church said. “And I don’t think it’s an easy policy for him to pull off.’’

Nader was more pessimistic.

“I just think these are just talking points, and [Trump] doesn’t even know how they would go about doing this,’’ she said.

Astead W. Herndon can be reached at astead.herndon@globe.com. Follow him on Twitter @AsteadWH.