The state of Illinois and the city of Chicago sued President Donald Trump on Monday, seeking to block the deployment of federalised National Guard troops to Chicago, as hundreds of National Guard troops from Texas headed to the nation's third-largest city.

Trump then escalated the widening clash with Democratic-led states and cities over the domestic use of military forces, threatening to invoke the Insurrection Act as a means to circumvent court restrictions on deploying troops where they are unwanted by local officials.

Illinois had sued in response to Pentagon chief Pete Hegseth's orders over the weekend to bring 300 Illinois National Guard members under federal control and then to mobilise another 400 Texas National Guard troops for deployment to Chicago.

While Illinois' request for a temporary restraining order plays out, U.S. lawyers told a court hearing on Monday that Texas National Guard troops were already in transit to the state. Trump then issued another memorandum calling up 300 Illinois National Guard troops, reinforcing Hegseth's previous order.

U.S. District Judge April Perry allowed the federal government to continue the deployment in Chicago while it responds to Illinois' suit. She set a deadline of midnight Wednesday for the U.S. to reply.

The Illinois dispute came after a federal judge in Oregon on Sunday temporarily blocked Trump's administration from sending any National Guard troops to police the state's largest city, Portland.

Shortly after Perry's ruling, Trump told reporters in the Oval Office he might invoke the Insurrection Act of 1792, which would allow troops to directly participate in civilian law enforcement, for which there is little recent precedent.

"I'd do it if it was necessary. So far, it hasn't been necessary. But we have an Insurrection Act for a reason. If I had to enact it, I'd do that," Trump said. "If people were being killed and courts were holding us up, or governors or mayors were holding us up, sure, I'd do that."

Later, when asked in an interview with Newsmax television whether he would invoke the law, Trump repeated that he would only use it if necessary, and then referenced Portland, Oregon, where the mayor and governor oppose deploying the National Guard to quell protests.

"If you take a look at what's been going on in Portland, it's been going on for a long time, and that's insurrection. I mean, that's pure insurrection," Trump said.

The law has been used sparingly, in extreme cases of unrest. The law was last invoked by President George H.W. Bush in 1992, when the governor of California requested military aid to suppress unrest in Los Angeles following the trial of Los Angeles police officers who beat Black motorist Rodney King.

Today, Democratic-led states and cities are pushing back against Trump's attempt to deploy military forces into cities, which the White House says are needed to protect federal government employees from "violent riots" and "lawlessness.”

Democratic leaders counter that their cities are being illegally targeted and falsely portrayed as awash in crime.

Trump has expanded the use of the U.S. military in his second term, which has included deploying troops along the U.S. border and ordering them to kill suspected drug traffickers on boats off Venezuela without due process.

National Guard troops are state-based militia forces that answer to their governors except when called into federal service.

Trump has ordered them to Los Angeles, Chicago, Washington, D.C. and Portland, prompting lawsuits from state and local leaders.

Chicago's lawsuit, is the fourth legal action opposing Trump's unprecedented use of soldiers to police U.S. cities. Courts have not yet reached a final decision in any of those cases, but judges in California and Oregon have made initial rulings that Trump likely overstepped his authority.

The Illinois lawsuit alleges the Republican president is deploying the military to Illinois based on a "flimsy pretext" that an ICE facility in a suburb of Chicago needs protection from protesters.

Illinois Governor J.B. Pritzker, in a press conference, accused Trump of unnecessarily escalating tensions by attempting to add National Guard troops to heavily armed federal police from Immigration and Customs Enforcement and other agencies already operating in Chicago.

Pritzker said those officers have fired tear gas and rubber bullets on peaceful protesters, with U.S. citizens, including children, being "traumatised and detained."

"Donald Trump is using our service members as political props and as pawns in his illegal effort to militarise our nation's cities,” Pritzker said.

"Donald Trump's deranged depiction of Chicago as a hellhole, a war zone and the worst and most dangerous city in the world was just complete BS," Pritzker said.

Trump, responding to Pritzker, reiterated his contention that Chicago was "like a war zone," saying Pritzker and Chicago Mayor Brandon Johnson had lost control.

"It's probably worse than almost any city in the world. You could go to Afghanistan, you can go to a lot of different places, and they probably marvel at how much crime we have," Trump said.