The newspaper wants to use a countersuit to get the Department of Justice to drop the lawsuit filed by the Trump administration last week.
"The lawsuit violates the constitutional rights of The New York Times and its journalists," the newspaper's lawyer David McCraw wrote in a statement.
When President Trump returned home from the NATO summit in Ankara last week, he travelled on an older Air Force One plane, not the donated plane from Qatar that he arrived on.
According to The New York Times, which cited sources close to the president, the switch was due to safety deficiencies in the new plane.
