The news outlets are seeking a temporary restraining order to block Trump's action in federal court in Washington, DC, with a hearing scheduled for Wednesday.
"This ban could not be a more direct assault on the First Amendment nor a more blatant violation of our most fundamental constitutional principles," the lawsuit says.
"Left unchallenged, this threatens press freedom and the public's right to independent journalism free from government interference," the outlets wrote in a joint statement.
"The government does not decide what the press reports or publishes."
Trump announced the ban on Friday on social media, saying those news outlets "shouldn't be able to constantly write or report FICTION and LIES when they're covering the President of the United States," and defended it in another post on Monday.
"The White House is not instituting an assault on the Free Press, something which I cherish. It is instituting an assault on the FAKE NEWS. It is a threat to our National Security, and must be stopped, NOW!" Trump wrote on Monday, without providing evidence of a national security threat.
Past presidents have battled with the media, but Trump's campaign has been unprecedented.
He has upended decades of tradition by denying basic access to many major news organisations, launching personal attacks on journalists for their reporting, filing lawsuits against media outlets, and elevating outlets seen as more sympathetic to the administration.
The White House launched a "Trump TV" stream on Monday evening, days after Trump banned the media outlets from the White House.
The White House said the stream would run videos and highlights of what it calls the Trump administration's achievements.
"This just makes it even clearer that the real goal here is to ensure that the American public is fed a steady diet of government propaganda," Jameel Jaffer, executive director of the Knight First Amendment Institute at Columbia University, said.
CNN is one of the five news organisations - along with ABC, CBS, Fox News and NBC - that make up the primary White House television pool.
They share the costs of covering the president, take turns organising coverage and share the footage with outlets around the country.
CNN had been scheduled to cover Trump's trip to New York for the United Nations General Assembly on Monday, but was not able to provide a pool feed.
In response, the other major TV networks suspended presidential pool coverage.
This effectively eliminated the most widespread video source for White House events just as Trump is set to meet numerous world leaders on the sidelines of the General Assembly and host Chinese President Xi Jinping in Washington later in the week.
"This is to advise that, effective today (Monday), the TV pool will not be covering events designated as pool coverage of the president," Bryan Boughton, who runs the Fox News Washington bureau and is the TV pool chair, said in an email.
Otherwise, it was business as usual in the White House press room on Monday as reporters planned for the day's events, including an afternoon ribbon-cutting ceremony for the Republican president's new Marine One helipad on the South Lawn.
The audio on the White House's own live stream of the ceremony, which it promoted as an alternative to the pool feed, was inaudible.
Trump's party is seeking to retain its narrow majorities in both chambers of Congress in the November midterm elections, but polls show the public souring on Republicans and Trump's own approval ratings stand near historic lows.
A person familiar with the matter, speaking on condition of anonymity, said Trump had been "very unhappy" with coverage of the midterm elections, the person said, and his frustration intensified after last week's Supreme Court ruling that blocked his attempt to limit mail-in voting.
with AP
