However, his attorneys have not filed any such requests with the court seeking to unseal the records, which are likely to contain damaging information about Trump.
Christina Bobb, the Trump attorney who signed the warrant materials on the day of the Aug. 8 search, appeared in the courtroom on Thursday to watch the proceedings.
She left without making any statements to reporters.
The former president has repeatedly claimed the search was politically motivated, and his son Eric Trump told Fox News that his father intends to release surveillance tape showing the FBI searching Mar-a-Lago "at the right time."
Trump has also tried to defend his actions, saying without providing evidence that he had a standing order to declassify the documents in question.
However, none of the three laws cited by the Justice Department in the search warrant require a showing that the documents were in fact classified.
Threats directed at FBI agents have increased since the raid.
In Ohio last week, police shot an armed man dead after he tried to breach an FBI building. A second man in Pennsylvania, meanwhile, has since been charged with making threats against FBI agents.
Bratt said on Thursday that the two agents whose names appeared on a leaked copy of the unredacted warrant have also since received threats.
In addition, he said, the department "is very concerned about the safety of the witnesses in the case."
Reinhart has also faced a barrage of criticism from Trump's supporters, who have publicly assailed his decision to approve the search warrant.
Trump's rhetoric against the FBI has caught on with Republican voters, 54% of whom say federal law enforcement officials behaved irresponsibly in the case, a Reuters/Ipsos poll found this week.
The FBI seized boxes containing 11 sets of classified materials at Mar-a-Lago, some of which were labeled "top secret" - the highest level of classification reserved for the most closely held US national security information.
Such documents usually are typically kept in special government facilities because disclosure could cause grave damage to national security.
Reinhart on Thursday also granted a request to unseal procedural records tied to the warrant, including the cover sheet and the government’s motion to seal the warrant. The cover sheet said the Justice Department is investigating the “willful” retention of national defense information, as well as the concealment or removal of government records and the obstruction of a federal investigation.