WASHINGTON—President Biden on Friday ordered the review and possible release of previously withheld government documents related to the Sept. 11 attacks on the Pentagon and the World Trade Center that could shed new light on the role of accomplices in the plot that killed nearly 3,000 people.

As the 20th anniversary of the attacks approaches, Mr. Biden ordered the Justice Department to consider declassifying additional materials contained in some of the Federal Bureau of Investigation’s case files of its investigation into the attacks that have long been sought as part a lawsuit brought by the families of 9/11 victims. The materials have been held back from disclosure in court on national security grounds.

Some families of the victims believe the long-sought files will provide additional transparency around Saudi links to the attacks. While most of the terrorists involved were from Saudi Arabia, the Saudi government has denied complicity in the attacks.

“The significant events in question occurred two decades ago or longer, and they concern a tragic moment that continues to resonate in American history and in the lives of so many Americans. It is therefore critical to ensure that the United States Government maximizes transparency,” Mr. Biden wrote in an executive order issued Friday.

The action by Mr. Biden fulfills a campaign-trail promise to the families of the victims of the attacks and could offer a new window into the government’s extensive investigation. In the weeks and months after 9/11, that probe consumed nearly all of the FBI’s resources and was the largest investigation in bureau history.

A flag was placed near a victim's name at the Sept. 11 Memorial in New York earlier this week, ahead of the 20th anniversary of the attacks.

Photo: Spencer Platt/Getty Images

Mr. Biden has been pressed by families of the Sept. 11 victims to act on that promise, with many signing an open letter last month saying he wouldn’t be welcome at any 20th anniversary commemorations of the attacks until he had declassified the records in question.

Families of the 9/11 victims have long sought more transparency about certain elements of the attacks, including access to secret government files about the potential role that Saudi Arabia played in the attacks.

In particular, the U.S. government has long withheld numerous documents on the attacks in litigation related to a federal lawsuit under the state secrets privilege, which allows the U.S. government to shield some material from being disclosed in court filings if it would do damage to national security. The lawsuit, which is still under way in federal court in New York, accuses the Saudi government of helping coordinate the 2001 suicide attacks.

In April 2020, the Trump administration invoked the privilege to avoid disclosing. Then-Attorney General William Barr also refused to publicly disclose the rationale for why the material needed to be withheld, writing that public discussion of the issues involved “would reveal information that could cause the very harms my assertion of the state secrets privilege is intended to prevent.”

James Kreindler, a lawyer who represents the families in the lawsuit, described Mr. Biden’s order as a “very positive” development but said he would withhold judgment until documents started to be released and he could evaluate how much material the government would redact from the documents.

During the 2020 campaign, Mr. Biden criticized the Trump administration’s stance in the litigation, writing in a letter to victims’ families: “I will direct my Attorney General to personally examine the merits of all cases where the invocation of privilege is recommended, and to err on the side of disclosure in cases where, as here, the events in question occurred two decades or longer ago.”

The impact of Mr. Biden’s order could be felt as soon as next week. The order specifies that the Justice Department’s review of a once-secret FBI evaluation of Saudi links must be completed by Sept. 11, 2021, the 20th anniversary of the attacks.

An internal FBI task force entitled Operation Encore looked at the potential role of Saudi nationals with possible connections to the government in assisting hijackers and issued an evaluation in 2016 that has long been withheld from the public and sought by families of the victims.

Write to Byron Tau at byron.tau@wsj.com