Trump said on social media that he "cherished" a free press but not "FAKE NEWS".
"White House access is a privilege - not a right," the administration posted on X.
The extraordinary ban of the three news outlets' reporters, which began over the weekend, represented a clear escalation of Trump's long-running efforts - in the courts and through administrative action - to restrict news coverage he finds objectionable.
They were also the latest test of First Amendment protections in the United States, where the government is constitutionally forbidden from restricting the press.
The 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 three outlets filed the joint lawsuit two days after their reporters were blocked from the White House and prevented from doing their jobs.
The reporters' entry badges were disabled on Saturday, a day after Trump had suddenly announced he was barring the outlets because of reporting he considered "fake news".
CNN is removed from pool duties, and other outlets take a stand in solidarity
On Monday morning, the banned TV networks were reporting from an intersection just outside the White House complex.
CNN, meanwhile, was removed from its pool duties, which are shared by the five major networks.
It had been scheduled to cover the president's trip to New York for the United Nations General Assembly. In an email to members, the TV pool said there would be no replacement coverage - and other networks would suspend their own pool coverage indefinitely.
"Effective today, the TV pool will not be covering events designated as pool coverage of the President," said the email from the current chair of the pool, Fox's Washington bureau chief, Bryan Boughton.
"This follows the White House's position preventing CNN from fulfilling its assigned pool duties."
Other news outlets also took steps in solidarity.
The AP joined a number of news organisations, including The Washington Post and The New York Times, in a decision not to publish photographs of presidential events on Monday.
The White House said on X: "The First Amendment protects their right to publish; it does not entitle them to a hard pass, briefing room seat, or place in the press pool."
On his Truth Social platform, Trump wrote that he was not attacking the First Amendment.
"The White House is not instituting an assault on the Free Press, something which I cherish," the president said.
"It is instituting an assault on the FAKE NEWS, something that has grown like Cancer in our beloved United States of America. It is corrupt, purposeful, pervasive, fully coordinated, and totally out of control. It is a threat to our National Security, and must be stopped, NOW!"
In his second term, Trump has upped the ante and punished certain media outlets and often lashed out at individual reporters in person or over social media, sometimes in strikingly personal terms - insulting them in briefings or in his recent speech at the White House Correspondents' Association dinner.
"This morning, we notified the government that we are filing a lawsuit today to protect our First Amendment rights and defend the principle that the government does not decide what the press reports or publishes," the banned outlets said in a joint statement posted early Monday on X.
"Left unchallenged, this threatens press freedom and the public's right to independent journalism free from government interference.
"This ban could not be a more direct assault on the First Amendment nor a more blatant violation of our most fundamental constitutional principles."
with AP
