The news outlets are seeking a temporary restraining order to block Trump's action in federal court in Washington DC and emergency hearings in the case could happen as soon as this week.
"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."
The US constitution, the banned news outlets said in their lawsuit, "does not allow a president or any other government official to deprive the press of their first amendment rights and liberty and property interests with no notice or process based solely on his dislike of the content of their reporting".
The outlets say the US government is constitutionally forbidden from restricting the press.
Trump announced the ban on Friday on social media and defended it in another post on Monday, claiming that news media posed a national security threat.
"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," Trump wrote on Monday.
"It is a threat to our National Security, and must be stopped, NOW!"
Past presidents have battled with the press, but Trump's campaign against the media has been unprecedented.
He has upended decades of tradition by denying basic access to major news organisations, criticising journalists personally for their reporting and also elevating new media outlets.
He has also filed a number of lawsuits against news organisations.
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, which had been scheduled to cover Trump's trip to New York for the United Nations General Assembly on Monday, was not able to provide a pool feed.
In response, the other major TV networks have suspended presidential pool coverage, effectively eliminating the most important video source for White House events.
"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 DC bureau and is the current TV pool chair, said in an email on Monday.
"This follows the White House's position preventing CNN from fulfilling its assigned pool duties," Boughton added.
"There will be no replacement pool put in place."
On Saturday, CNN, MS NOW and Politico said their journalists were turned away from the White House grounds and had their press credentials confiscated.
Over the weekend, they stationed journalists across the street from the White House and continued coverage.
During his first term in office, Trump sought to revoke or suspend White House credentials of two correspondents for CNN and Playboy magazine but federal judges ordered their passes restored.
with AP
