US President Donald Trump has already sent troops onto the streets of Los Angeles and Washington, DC and has ordered them to Memphis as well as Chicago and Portland, threatening to invoke emergency powers to forward such efforts if the courts get in the way.

Trump -- who suggested last week that American cities be used as "training grounds" for US military forces -- exaggerated the scale of unrest in Los Angeles and crime in Washington to justify those deployments, and a judge suggested he did the same when it comes to Portland.

The troops from Texas were sent to Illinois as part of a mission to protect "federal functions, personnel, and property," the Pentagon official said on condition of anonymity, adding that the Guardsmen have been mobilized for an initial period of 60 days.

The troops were seen on Tuesday at a military facility in Elwood, southwest of Chicago.

The planned deployment of these forces has infuriated Democratic Governor JB Pritzker, who said they "should stay the hell out of Illinois," and that any deployment against his state government's wishes would amount to an "invasion."

Trump over the weekend authorized the deployment of 700 National Guard troops to Chicago, sparking a lawsuit by Illinois state officials who accused him of using US troops "to punish his political enemies."

- 'Untethered to the facts' -

"The American people, regardless of where they reside, should not live under the threat of occupation by the United States military, particularly not simply because their city or state leadership has fallen out of a president's favor," the Illinois Attorney General and counsel for Chicago said.

But Judge April Perry, an appointee of Trump's Democratic predecessor Joe Biden, declined to issue an immediate temporary restraining order, instead scheduling a full hearing for Thursday.

Homeland Security Secretary Kristi Noem has defended the plan to send troops to Chicago, claiming that the third-largest US city is "a war zone."

Trump has similarly taken aim at Portland, which like Chicago has seen surges of federal agents as part of the president's mass deportation drive, prompting protests outside immigration processing facilities. Trump asserted that it is "war-ravaged" and riddled with violent crime.

But in a Saturday court order temporarily blocking the deployment of troops to Oregon, US District Judge Karin Immergut wrote that "the President's determination was simply untethered to the facts."

Protests in Portland did not pose a "danger of rebellion" and "regular law enforcement forces" could handle such incidents, the judge wrote.

Trump responded to that setback by openly mulling the use of the Insurrection Act -- which allows the president to deploy the military within the United States to suppress rebellion -- in order to send more troops into Democratic-led US cities.

"We have an Insurrection Act for a reason," Trump said, adding that he would use it if "people were being killed and courts were holding us up or governors or mayors were holding us up."