Several members of the House and Senate, including House Democratic leader Nancy Pelosi, have joined 9/11 families in pressuring for declassification of 28 pages that are part of government documents compiled on the 9/11 attack amid speculation of a possible role by Saudi Arabia.
Nearly 3,000 people were killed in the attack.
In an interview with CBS's Charlie Rose, Obama was asked if had read the 28 pages. "I have a sense of what's in there," he replied.
"My understanding is that he's about to complete that process," the president said.
Former US Sen Robert Graham, who helped write the report that includes the 28 redacted pages, recently told CBS's "60 Minutes" the secret material could reveal possible Saudi backing for the men who hijacked airplanes, flying two into the World Trade Center in New York and another into the Pentagon.
A third hijacked plane crashed on September 11, 2001, in western Pennsylvania.
Obama also voiced concerns about a legislative move to allow victim families to bring lawsuits against other countries believed to have provided support for attacks.
"This is a matter of how generally the United States approaches our interactions with other countries," he said.
"If we open up the possibility that individuals and the United States can routinely start suing other governments, then we are also opening up the United States to being continually sued by individuals in other countries."
Material from the interview was to be broadcast on "CBS This Morning" and PBS, as well as "CBS Evening News with Scott Pelley.