The news outlets asked a judge overseeing their case in Washington, DC, federal court to grant a preliminary injunction blocking Trump's bans until there is a final ruling in the case.
US District Judge Timothy Kelly previously issued a 14-day temporary restraining order blocking the bans, finding they likely violated the news outlets' rights to fair legal treatment.
The outlets said in their September 21 lawsuit that Trump's bans were unlawful viewpoint discrimination under the First Amendment of the Constitution, which guarantees free speech and free press rights.
"The president and his administration have continued to make clear that this ban has only one purpose: to punish reporting he doesn't like," said Theodore J. Boutrous, the plaintiffs' lead lawyer.
"That's retaliation and viewpoint discrimination, pure and simple," Boutros said. "With the district court's temporary restraining order expiring this week, it is critical to ensure that the White House continues to be prevented from implementing this unconstitutional ban on the free press."
The Justice Department said Trump lawfully banned the outlets after determining their coverage threatened national security by revealing classified information.
Trump said in a September 18 social media post that he was banning the outlets for "reporting FAKE NEWS" and that they "shouldn't be able to constantly write or report FICTION and LIES."
Trump has frequently clashed with the media in his second term and personally sued outlets including the New York Times, Wall Street Journal and BBC for defamation.
The Trump administration has until Friday to respond to Monday's filing, and the media outlets will submit a final written brief by October 5.
Kelly said he would schedule a hearing and that he planned to rule "expeditiously."
with AP
