President Donald Trump has called for the jailing of Illinois officials, accusing them of not doing enough to ensure the safety of federal immigration officers who are conducting raids in Chicago.

The president wrote in a social media post that Chicago Mayor Brandon Johnson and Illinois Governor JB Pritzker, both Democrats, "should be in jail for failing to protect Ice Officers!"

Trump has previously called the city a "war zone" amid protests against immigration enforcement.Pritzker has called the president's actions "authoritarian".

The Republican president spoke as hundreds of National Guard troops arrived in the city as part of his immigration crackdown.

The standoff raises the temperature in an already heated rhetorical battle between Trump and local officials in Democratic-led cities and states.

The Chicago mayor quickly fired back at Trump, saying "this is not the first time Trump has tried to have a Black man unjustly arrested. I'm not going anywhere."

Pritzker vowed: "I will not back down.

"Trump is now calling for the arrest of elected representatives checking his power. What else is left on the path to full-blown authoritarianism?"

The arrival of National Guard troops in Chicago follows similar deployments to Los Angeles and Washington DC to stem what the president has described as "out of control" crime. 

Last month, Washington DC Attorney General Brian Schwalb filed a lawsuit challenging the deployment, saying "it is not only unnecessary and unwanted, but it is also dangerous and harmful to the District and its residents". 

Trump has also directed them to enter Memphis, Tennessee, and Portland, Oregon. A judge has blocked their deployment to Portland, but allowed them to go to Chicago for now.

The state of Illinois and the city of Chicago filed a lawsuit on Monday to block the deployment. A hearing is scheduled for Thursday. 

Trump has threatened to invoke the Insurrection Act and use the military if courts stop the deployments, which he has defended as necessary to address rampant crime and defend immigration enforcers.

"If I had to enact it, I'd do it, if people were being killed and courts were holding us up, or governors or mayors were holding us up," Trump said on Monday.

White House officials have repeatedly criticised legal efforts to block the deployment, with deputy chief of staff Stephen Miller telling reporters this week that court rulings against the government's law enforcement efforts were tantamount to "an insurrection against the laws and Constitution of the United States".

In Chicago, protests grew violent last weekend, with immigration authorities saying they opened fire on a woman after she and others allegedly rammed their cars into law enforcement vehicles. 

The woman's condition is unclear, but officials said she drove herself to hospital. Her attorney has disputed the government's version of events.

President Trump is expected to host a roundtable on combating Antifa - a loosely-organised coalition of far-left activists - on Wednesday afternoon.