FBI agents who searched former President Donald Trump’s Mar-a-Lago home Monday removed 11 sets of classified documents, including some marked as top secret and meant to be only available in special government facilities, according to a search warrant released by a Florida court Friday.

The Federal Bureau of Investigation 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 which was granted by a federal magistrate judge in Florida.

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.

Mr. Trump’s lawyers argue that the former president used his authority to declassify the material before he left office. While a president has the power to declassify documents, there are federal regulations that lay out a process for doing so.

“They could have had it anytime they wanted—and that includes long ago. All they had to do was ask,” Mr. Trump said in a statement issued Friday.

On Friday afternoon, U.S. Magistrate Judge Bruce Reinhart issued an order making the warrant and inventory list public, after the Justice Department said in a court filing that Mr. Trump’s lawyers told federal prosecutors they didn’t object to the government’s request to unseal the information.

The search and seizure warrant, signed by Judge Reinhart, shows that FBI agents sought to search “the 45 Office,” as well as “all storage rooms and all other rooms or areas within the premises used or available to be used by [the former president] and his staff and in which boxes or documents could be stored, including all structures or buildings on the estate.”

They didn’t seek access to search private guest rooms, such as those of Mar-a-Lago members, according to the document.

The former president and his team don’t have the affidavit, which would provide more detail about the FBI’s investigation, according to people familiar with the process. An affidavit 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 lawyers have asked for a more specific account of what was removed from Mar-a-Lago.

The disclosure of the warrant and the inventory marks the culmination of an extraordinary week, which began last Friday at 12:12 p.m., when the judge signed off on the unprecedented warrant to search a former president’s home. Three days later, at 6:19 p.m., a lawyer for Mr. Trump, Christina Bobb, signed a receipt for the items the FBI took that day.

Former President Donald Trump, departing Trump Tower in New York Wednesday, has said he wouldn’t oppose releasing the search warrant.

Photo: Julia Nikhinson/Associated Press

To the Justice Department, the search was the result of a monthslong effort to get the classified documents remaining in Mr. Trump’s possession after at least two prior attempts. They were at first primarily interested in securing the documents, but pursued a criminal investigation as they began to doubt that Mr. Trump’s team was being forthright about the documents still in their possession, people familiar with the matter said.

To Mr. Trump’s allies, the search was a heavy-handed approach to obtaining documents they say Mr. Trump was willing to return and was in the process of negotiating the return.

It is unclear how the investigation may progress and whether prosecutors are considering bringing any charges against Mr. Trump or others in connection with the investigation now that the documents have been recovered.

Rep. Markwayne Mullin (R., Okla.)—who sits on the House Intelligence Committee and has questioned the need for the search by federal agents—said Attorney General Merrick Garland should brief the Intelligence Committee. “It’s a high threshold to say it was an immediate national security threat, if it wasn’t an immediate national security threat then I think there’s a lot of questions that need to be answered,” he said.

The warrant said investigators were seeking all records that could be evidence of violations of laws governing the gathering, transmitting or losing of classified information; the removal of official government records; and the destruction of records in a federal investigation.

The U.S. government has three main levels of classification. In ascending order, the levels are confidential, secret and top secret. They are designed to reflect how sensitive a document’s underlying contents are considered, meaning that a breach of a higher classification level could potentially cause more damage to national security.

SCI documents are typically reserved for military, civilians with special clearance, and contractor personnel who work in a Sensitive Compartmented Information Facility, or SCIF, including those who are responsible for the security of a SCIF.

As the investigation progressed, someone familiar with the stored papers told investigators there may still be more sensitive documents on the premises beyond what they had already received in January and June, people familiar with the matter have said.

It is not known when the documents stored at Mar-a-Lago arrived there, during Mr. Trump’s presidency or as he left office.

Mr. Stone didn’t immediately respond for comment.

Mr. Trump, while in office, would regularly feud publicly with French President Emmanuel Macron over Twitter about various policy disagreements, particularly trade and Mr. Trump’s decision to withdraw from the Iran nuclear agreement. Privately, Mr. Trump used to tell aides that he believed Mr. Macron to be a “leaker” and untrustworthy, according to several former officials. The French embassy didn’t immediately respond for comment.

The search, while Mr. Trump was in New York, stoked a political firestorm with Republican lawmakers demanding an explanation for the unprecedented search of a former president’s home. The showdown began after the National Archives in January retrieved more than a dozen boxes of White House documents from the resort earlier this year, some of which officials deemed classified national-security information.

Mr. Garland and FBI officials deliberated for days about whether to respond to the criticism of the search and how much to say, people familiar with discussions said. The attorney general ultimately decided to let the Justice Department’s work speak for itself and directed the agency to request the warrant be unsealed.

Millions of people in the U.S. hold some level of clearance that grants them access to classified documents, though far fewer have access to the highest levels. While intelligence agencies can declassify information and release it to the public, the process for doing so is often slow and may require multiple intelligence agencies to sign off.

A list of documents recovered from former President Donald Trump’s Mar-a-Lago resort in Palm Beach, Fla., cites 20 boxes of items, binders of photos and a handwritten note.

Photo: giorgio viera/Agence France-Presse/Getty Images

A sitting president generally has the authority to unilaterally declassify any material of his or her choosing, but such a privilege is rarely used. Mr. Trump at times did disclose classified information during his time in office, including when he tweeted a surveillance satellite image showing damage at an Iranian space facility.

While a president has the power to declassify documents, federal regulations lay out a process for doing so. Those rules must be followed for a declassification to become legally effective, said Dan Meyer, a national-security lawyer at Tully Rinckey in Washington.

Once Mr. Trump left office on Jan. 20, 2021, he became bound by the same rules as other private citizens, Mr. Meyer said.

—Vivian Salama and Dustin Volz contributed to this article.

Write to Alex Leary at alex.leary@wsj.com, Aruna Viswanatha at Aruna.Viswanatha@wsj.com and Sadie Gurman at sadie.gurman@wsj.com