WASHINGTON—A federal judge in Florida will hear arguments Thursday over whether to make public the affidavit laying out what evidence led to the extraordinary FBI search of former President Donald Trump’s Mar-a-Lago home, as investigators begin to pore over documents and other items seized from the sprawling private club.

The affidavit would provide more detail about the FBI’s investigation than what is contained in the search warrant unsealed last week by U.S. Magistrate Judge Bruce Reinhart, which revealed that agents removed from the property 11 sets of classified documents, including some marked as top secret and meant to be only available in special government facilities.  

The Justice Department has asked Judge Reinhart, who approved the initial warrant to search, not to unseal the affidavit, saying its release would “compromise future investigative steps” and “likely chill future cooperation by witnesses whose assistance may be sought as this investigation progresses.” 

In a Monday filing, prosecutors said that they wouldn’t object to making public some other, less sensitive information associated with the warrant, but that the affidavit itself would serve as “a road map to the government’s ongoing investigation,” which they described as an intensive probe involving highly classified information.

The warrant itself was unsealed only after the Justice Department urged Judge Reinhart to release it, a move Attorney General Merrick Garland said he directed in light of Mr. Trump’s confirmation of the search on the day it happened and the “substantial public interest” in the matter.

Monday’s filing came in response to requests from media outlets, including The Wall Street Journal, to make public the document, which would explain what evidence, including witnesses, the government had collected and describe why investigators believe that a crime may have been committed. 

Mr. Trump’s and his supporters, including some in Congress, have also pushed for the release of the affidavit, as political fervor over the Aug. 8 search, which set off a furious political response with the former president’s supporters and Republican lawmakers accusing the Justice Department of overreach.

In a posting on his social-media platform early Tuesday, the former president said, “I call for the immediate release of the completely Unredacted Affidavit pertaining to this horrible and shocking BREAK-IN.”

Justice Department officials have defended the Mar-a-Lago search as a necessary step approved by Mr. Garland himself after weeks of deliberation.

People familiar with the Justice Department’s approach have said a primary goal of the search was to ensure the security of highly sensitive national-security documents after the Trump team didn’t relinquish them and amid concerns that the security of the material at Mar-a-Lago had been put at risk.

FBI agents took around 20 boxes of items, binders of photos, a handwritten note and the executive grant of clemency for Mr. Trump’s ally Roger Stone, a list of items removed from the property shows. Also included in the list was information about the “President of France,” according to the three-page list. The list is contained in a seven-page document that also includes the warrant to search the premises. 

The list includes references to one set of documents marked as “Various classified/TS/SCI documents,” an abbreviation that refers to top-secret/sensitive compartmented information. It also says agents collected four sets of top secret documents, three sets of secret documents and three sets of confidential documents. The list didn’t provide any more details about the substance of the documents.

Alex Leary contributed to this article.

Write to Sadie Gurman at sadie.gurman@wsj.com