Tensions between President Trump and Illinois leaders escalated on Saturday when the White House posted an image on social media depicting Mr. Trump with helicopters, billowing flames and the Chicago skyline.

“Chicago about to find out why it’s called the Department of WAR,” read the post, titled “Chipocalypse Now,” a reference to the 1979 war movie “Apocalypse Now.”

The threat from the president came after weeks of the Trump administration’s promising to crack down on illegal immigration in Chicago, part of a campaign vow from Mr. Trump to more rigorously enforce immigration laws across the country.

It was uncertain when the escalated effort by Immigration and Customs Enforcement might begin, and officials declined to comment on Saturday afternoon.

Elected officials in Chicago and advocates for immigrants said that they were watching closely for signs of heightened enforcement and that they had not seen anything out of the ordinary. There were no confirmed reports of increased ICE activity in Chicago, said Cassio Mendoza, a spokesman for Mayor Brandon Johnson.

Mr. Johnson, a Democrat, said on social media that Mr. Trump’s latest post was “beneath the honor of our nation, but the reality is that he wants to occupy our city and break our Constitution.”