Cohen, who is under criminal investigation for possible bank fraud and campaign finance violations, wants the material to be reviewed before federal prosecutors have a chance to scrutinise it.
Cohen has asked for a court-appointed outside lawyer to serve as special master and review the material first, or for his own lawyers to review the documents so they can tell prosecutors which documents are covered by attorney-client privilege.
Cohen attended today's hearing. Also on hand was adult-film star Stormy Daniels, whom Cohen secretly paid US$130,000 in 2016 to keep quiet the details of an alleged sexual liaison she had with Trump.
Yesterday, other lawyers representing Trump filed a letter to US District Court Judge Kimba Wood, the judge overseeing the case, arguing that the President should be allowed to review the material before Justice Department lawyers.
As part of the judge's effort to resolve such requests, she asked Cohen's lawyers to tell her how many clients, and documents, might be involved in the material seized by the FBI. Earlier, Cohen's lawyers suggested there could be thousands or millions of documents covered by lawyer-client privilege.
The letter from Cohen's lawyer Todd Harrison filed today said agents seized "more than a dozen electronic devices and other items that include documents and data regarding topics and issues that have nothing to do with" the material sought in the search warrant.
The letter says that from 1996 to 2006, Cohen had hundreds of clients, adding that he did not know if any material from those old clients were in the seized files. From 2007 to 2017, Cohen worked as a lawyer for Trump and the Trump Organisation.
The letter said that in 2017 and 2018, Cohen had "at least 10 clients," but seven of those were business consulting clients whose work did not involve legal advice.
The three other clients, according to the letter, are Trump, Broidy and a third client whom Cohen initially did not want to be identified.
Cohen helped Broidy negotiate a US$1.6 million settlement with a former Playboy model who got pregnant after they had an affair.
"As to the one unnamed legal client, we do not believe that Mr. Cohen should be asked to reveal the name or can permissibly do so," the letter said. "Upon information and belief, the unnamed legal client's matters are responsive to any matter covered by . . . the search warrants."
Cohen's lawyers argue that if the court appoints a special master to oversee the issue, "that legal client would allow their name to be disclosed to the special master."
In making their requests, Trump and Cohen contend that the Justice Department policy is unfair and infringes on constitutional protections.
It is unusual but not unprecedented for criminal investigators to seize documents from a lawyer, and there is a policy in place designed to shield information covered by the lawyer-client privilege.
That procedure involves having a "taint team" — also referred to as a "filter team" of prosecutors outside the investigation review all the material and separate what is covered by the privilege. A lawyer's communications with a client are not covered by the privilege if those discussions do not involve legal advice, or were used to further a crime or fraud.
Under the procedure, the taint team would turn over to the case investigators all the material that is relevant and not covered by attorney-client privilege.
"The President objects to the government's proposal to use a 'taint team' of prosecutors from the very office that is investigating this matter to conduct the initial privilege review of documents seized from the President's personal attorney, Michael Cohen,'' Trump lawyer Joanna Hendon wrote to the judge.
She added that "the President respectfully requests" that the judge issue an order barring the taint team from conducting an initial review of the seized material and require the government to turn over a copy of that material to Cohen's lawyers.
Then, the President wants the court to direct Cohen "to identify to the President all seized materials that relate to him in any way and to provide a copy of those materials to him and his counsel," according to the letter. Any disputes about what material was or wasn't covered by the lawyer-client privilege would then be decided by a judge, under the President's proposal.
People familiar with the Cohen investigation have said he is being investigated for possible bank and wire fraud. Prosecutors are examining whether crimes were committed as part of any pattern or strategy of trying to buy the silence of people who could offer accounts that could have damaged Trump's candidacy in 2016.
In addition, the FBI is also looking into whether any fraud was committed in connection with Cohen's ownership of taxi medallions — assets whose value has plummeted in recent years.