But on Tuesday night, the Justice Department used a routine court filing in the matter to initiate a blistering counteroffensive that disclosed new evidence that Mr. Trump and his legal team may have interfered with the inquiry.

In the filing, in Federal District Court for the Southern District of Florida, department officials revealed more details about the classified materials that Mr. Trump had taken from the White House, including a remarkable photograph of several of them arrayed on the floor of Mar-a-Lago, his home and private club in Florida. In what read at times like a road map for a potential prosecution down the road, the filing also laid out evidence that Mr. Trump and his lawyers may have obstructed justice.

It was as if Mr. Trump, seeming not to fully grasp the potential hazards of his modest legal move, cracked open a door, allowing the Justice Department to push past him and seize the initiative.

“The Trump team got more than they bargained for,” said Preet Bharara, a former U.S. attorney in Manhattan and a longtime critic of Mr. Trump. “In response to a thin and tardy special master motion, D.O.J. was given the opportunity to be expansive.”