Federal agents this past week seized materials largely focused on Michael Cohen’s “personal business dealings” as part of a grand-jury investigation into President Donald Trump’s longtime lawyer, prosecutors revealed for the first time in a filing Friday, as a dispute between the government and Mr. Cohen’s attorneys unfolded in federal court.

The filing from the Manhattan U.S. attorney’s office said prosecutors had undertaken a monthslong investigation of Mr. Cohen for “criminal conduct,” and followed the seizure earlier this week of documents and information from three locations as well as a safe-deposit box and two cellphones.

The Manhattan U.S. attorney’s case followed a referral by Special Counsel Robert Mueller’s office.

The filing on Friday came in response to a request by Mr. Cohen’s lawyers for a temporary restraining order to stop the U.S. attorney’s office from reviewing the seized evidence before Mr. Cohen’s lawyers or a third party could sort through it first for communications protected by attorney-client privilege.

Mr. Cohen’s lawyers are opposing the government’s use of a “filter team” of prosecutors who are walled off from the investigation to review the seized materials for privileged documents.