The flags were lowered to half-staff this morning.
The president said in the Rose Garden that he met today with the director of the Federal Bureau of Investigation, Robert Mueller, and representatives of relevant agencies to discuss the ongoing investigation of the massacre.
"We don't know all the answers yet, and I would caution against jumping to conclusions until we have all the facts," said Mr. Obama.
"What we do know is that there are families, friends and an entire nation grieving right now for the valiant men and women who came under attack yesterday in one of the worst mass shootings ever to take place on an American military base," he said.
He called the decision to lower the flags a "modest tribute" to those who were killed as well as "a recognition of the men and women who put their lives on the line every day to protect our safety and uphold our values."
"We honor their service, we stand in awe of their sacrifice, and we pray for the safety of those who fight, and for the families of those who have fallen," said Mr. Obama.
The president said the administration would continue to provide updates about the situation in the coming days and weeks. He went on to discuss this morning's jobs report and a bill he signed to extend unemployment benefits.