Lawyers for President Donald Trump say they should be allowed to review the material seized by the Federal Bureau of Investigation last week from Mr. Trump’s longtime lawyer Michael Cohen before government investigators begin their own examination, according to a court filing late Sunday.

The filing asks​ a Manhattan federal judge to stop the government from using a “taint team” of prosecutors to review the evidence for documents protected by attorney-client privilege and to issue an order allowing Mr. Cohen, Mr. Trump and their legal teams to comb through it first for “materials over which the President asserts privilege.”

After Mr. Trump identifies which communications he believes are privileged, the government taint team can make objections, the filing said, and the court can make the final determination about which materials investigators are allowed to see.

The government is expected to respond to the filing Monday morning.

On April 9, FBI agents raided the office, home and hotel room of Mr. Cohen, as part of an ongoing grand-jury investigation by the Manhattan U.S. attorney’s office into Mr. Cohen.