A federal judge in Florida will hear arguments on Thursday over whether to make public an affidavit used to justify a search of Donald Trump’s Florida estate, as broadening legal disputes on multiple fronts intensify against the former president and his allies.

In a 13-page filing on Monday, the justice department objected to efforts to unseal the document, arguing that doing so would “jeopardize the integrity of this national security investigation” into Trump’s handling of some of the government’s most closely held records after leaving the White House. The prosecutors said that the affidavit that gave the FBI probable cause to search Trump’s Mar-a-Lago resort contained sensitive information about witnesses who are key and acknowledged that its investigation involved “highly classified material”.

Bruce Reinhart, the federal magistrate judge who signed off on the search warrant, will decide whether to publish the affidavit, which would provide more details about the investigation and the FBI’s search of Trump’s private residence. Trump and his allies, including some members of Congress, have also pushed for the release of the affidavit.

But the prosecutors said the affidavit should not be unsealed because that could reveal the scope of the investigation into Trump’s unauthorized retention of classified White House records.

“The affidavit would serve as a roadmap to the government’s ongoing investigation, providing specific details about its direction and likely course,” prosecutors wrote. They also argued that releasing the document could compromise the continuing investigation.

“Disclosure of the government’s affidavit at this stage would also likely chill future cooperation by witnesses whose assistance may be sought as this investigation progresses, as well as in other high-profile investigations,” prosecutors added.

Last week, Reinhart agreed to unseal the search warrant and a list of items removed from the property after the justice department, in a rare move, asked for the documents to be made public given the “substantial public interest” in the investigation. Trump did not oppose the release of the materials, which he had refused to disclose publicly.

FBI agents seized about 20 boxes of materials, among them documents designated “top secret”, a grant of clemency for Trump’s close ally, Roger Stone, and information related to the “president of France”, according to the list of items removed from the property. The search warrant, unsealed on Friday, revealed that federal agents were investigating potential violation of the Espionage Act, among other laws.

Trump has sought to cast himself as a victim of a political witch-hunt designed to keep him from running for office, even as his campaign gleefully shares news stories claiming his recent legal troubles have only served to strengthen his support.

The tussle over the affidavit is only the latest in a series of legal obstacles that could trip up Trump and his closest allies.

This week, Trump’s former attorney Rudy Giuliani was informed that he is a target of a criminal investigation in Georgia related to efforts by the former president and his legal team to invalidate Joe Biden’s electoral victory in the state. The notification came as a federal judge rejected an attempt by the Republican senator Lindsey Graham, another prominent Trump ally, to avoid testifying in the same investigation before the special grand jury in Atlanta.

As his personal lawyer, Giuliani led the efforts to keep Trump in power, which included brazen attempts to overturn the results of elections in key states that Trump lost. Giuliani, the former mayor of New York City, is scheduled to testify before the special grand jury in Atlanta on Wednesday. He is expected to invoke attorney-client privilege on questions related to his discussions with Trump over those efforts, the Guardian has reported.

Meanwhile, Trump took a similar approach when questioned under oath last week in New York state’s long-running civil investigation into his business practices. In a statement, Trump claimed to have done nothing improper but invoked his fifth amendment right against self-incrimination.

And all that comes against the backdrop of the justice department’s intensifying investigation into the January 6 attack on the US Capitol and Trump’s attempts to reverse his defeat. The New York Times on Monday reported that Eric Herschmann, a lawyer who worked in the Trump White House, had been subpoenaed by a federal grand jury. Pat Cipollone, who served as White House counsel, has also received a subpoena, according to the Times.

Trump and his allies have attacked the various legal investigations as politically motivated and denied wrongdoing.