The media companies are seeking to have a federal judge overturn the decision the president made on Friday.
Despite valid accreditation, journalists from the three companies were denied entry to the White House on Saturday.
In the lawsuit, they write jointly that the decision is a "direct attack on the constitution."
According to Trump, the reason for the ban is "their constant 'reporting' of fake news."
"Media should not be able to constantly write or report fiction and lies when covering the President of the United States, the Trump administration, or the United States," the president wrote on Truth Social on Friday, partly in capital letters.
