US President Donald Trump on Monday said he plans to send federal law enforcement personnel into more major US cities, despite a growing controversy over the officers' recent presence in Portland, Oregon.

"We're sending law enforcement," Trump told reporters at the White House. "We can't let this happen to the cities."

Trump mentioned New York, Chicago, Philadelphia, Detroit, Baltimore and Oakland as possible destinations for federal forces, adding that the cities' mayors are "liberal Democrats".

Mayors in some of those cities responded Monday with a letter to Attorney General William Barr and to Chad Wolf, acting secretary of the Department of Homeland Security (DHS), that said: "The unilateral deployment of these forces into American cities is unprecedented and violates fundamental constitutional protections and tenets of federalism. As you are well aware, President Trump threatened to deploy federal forces in Seattle to "clear out" a protest area and in Chicago to "clean up" the city.

"Seattle and Chicago authorities objected and threatened legal action to stop such actions. In Washington, DC outside Lafayette Park, extreme action was taken by federal law enforcement against protesters without the Mayor of DC's approval," the letter said.

It was signed by Chicago Mayor Lori Lightfoot, Atlanta Mayor Keisha Lance Bottoms, Portland Mayor Ted Wheeler, Seattle Mayor Jenny Durkan, Washington Mayor Muriel Bowser, and Quinton Lucas, the mayor of Kansas City, Missouri.

A constitutional law expert said Monday that the situation could become a test case of states' rights.

"The idea that there's a threat to a federal courthouse, and the federal authorities are going to swoop in and do whatever they want to do without any cooperation and coordination with state and local authorities is extraordinary outside the context of a civil war," said Michael Dorf, a professor of constitutional law at Cornell University.

Senator Rand Paul, a Kentucky Republican often supportive of libertarian principles, also opposed sending federal agents to cities.

"We cannot give up liberty for security. Local law enforcement can and should be handling these situations in our cities but there is no place for federal troops or unidentified federal agents rounding people up at will," Paul tweeted.

Of law enforcement sent to Portland, Trump said, "They've been there three days and they really have done a fantastic job in a very short period of time, no problem. They grab a lot of people and jail the leaders. These are anarchists."

Federal officers last week began cracking down on the protests in Portland against police brutality and racism, using tear gas and taking some activists into custody.

Protests across the US started after the May 25 killing of George Floyd, a black man, during an arrest by police in Minneapolis.

State and local leaders in Oregon, as well as members of Congress, have called for Trump to remove DHS officers from Portland.

DHS officials said Monday that they would not back down and would not apologize.

Trump also criticized New York Governor Andrew Cuomo over rising crime in New York City. The Republican president previously has had numerous clashes with the Democratic governor over the handling of the COVID-19 pandemic.

Trump said that if Cuomo doesn't reverse a spike in violent crime in New York City, he will send in federal authorities.

Trump told reporters in the Oval Office he was upset by reports that a 33-year-old Brooklyn woman, Shatavia Walls, was fatally shot after complaining about illegal fireworks. He said the NYPD is "afraid to do anything".

"We can't let this happen to the cities. New York was up 348 percent, the crime wave. So the governor has to do something about it. And if the governor is not going to do something about it, we'll do something about it.

"But what's happening in New York, a place I love — I love New York. Look at what's going on over there. The woman who was shot because she said, 'Could you please not light off firecrackers?' And they turned around and shot her eight times and she died. That's not our civilization, that's not about us," he told reporters.

"And then the police are afraid to do anything. I know New York very well, I know the police very well, New York's Finest, and the fact is, they're restricted from doing anything, they can't do anything."

While Cuomo hadn't responded by Monday evening, New York Mayor Bill de Blasio tweeted: "We've seen the chaos secret police are creating in Portland. We won't let it happen here."

Trump also spoke of rising violent crime in Chicago and suggested that Democratic presidential candidate Joe Biden wouldn't address it.

"If Biden got in, that would be true for the country, the whole country would go to hell, and we're not going to let it go to hell," Trump said.

Biden had not responded as of 8 pm Monday.

In Seattle on Sunday, a "well organized" group marched through the downtown area to Capitol Hill, damaging businesses and the Seattle Police Department's West and East precincts, according to a police spokesperson, NBC affiliate king5.com reported.

Twelve Seattle police officers were injured in the clashes.

A group of peaceful protesters had gathered in Westlake Park before a separate group arrived carrying baseball bats and was set out for "destruction and damage", Seattle police said.

Police said the group attacked  an Amazon store and a Starbucks. The Macy's department store downtown also had windows broken, king5 reported.

Reuters and The Associated Press contributed to this story.