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The Justice Department filing was in response to a request by Cohen for a temporary restraining order that would prevent law enforcement from reviewing certain material seized by FBI agents on Monday.
FBI agents searched Cohen's home, hotel room, office, a safety deposit box and seized two cellphones in a raid on Monday that drew a furious reaction from Trump.
Trump denounced the FBI raid on "good man" Cohen as "disgraceful" and an "attack on our country." Cohen has been Trump's personal lawyer for years and has acknowledged making a $130,000 payment before the 2016 election to porn star Stormy Daniels, who says she had a tryst with Trump a decade ago.
Cohen has long been known as Trump's rough-and-tumble "fixer" dedicated to protecting his boss's interests.
Cohen's lawyer cited attorney-client privilege in seeking to restrict access to "documents and communications related to numerous clients."
But the government said Cohen appears to have only one client -- Donald Trump.
"The (US Attorney) and FBI have reason to believe that Cohen has exceedingly few clients and a low volume of potentially privileged communications," the Justice Department motion said.
"It is neither apparent that Cohen, in his capacity as an attorney, has many, or any, attorney-client relationships other than with President Donald Trump," it said.