Speaking to journalists in the Oval Office, Obama said there may have been "mixed motives" behind the shooting, a factor that is complicating the investigation.
"It is possible that this was terrorist-related, but we don't know. It's also possible this was workplace-related," Obama said after a meeting with his national security team. Obama said the suspects in the Wednesday shooting were equipped with weapons at the time they were killed by police and appeared to have access to more at home.
"We don't know why they did it. We don't know at this point the extent of their plans," Obama said, warning against passing judgment before conclusions are drawn.
Obama repeated his case for new gun control measures - a call he's promised to issue after every mass shooting - although he did not lay out specific proposals or criticize the Republican-led Congress for blocking tighter controls, as he often does.
Speaking softly, a subdued Obama said too often Americans feel there's nothing they can do to prevent this kind of violence.
"We all have a part to play. As the investigation moves forward, it's going to be important for all of us, including our legislatures, to see what we can do to make sure that when an individual decides they want to do somebody harm, we make it a little harder for them to do it. Right now, it's just too easy.
"We're going to have to, I think, search ourselves as a society," he said.
Obama ordered U.S. flags at the White House and other government buildings to be flown at half-staff through Monday to honor the victims of the shootings.