Dan Pfeiffer, an assistant and advisor to the president, said this on CBS television's "Face the Nation" programme, adding that Pentagon officials were against arming soldiers inside the base in the wake of the shooting.
A Fort Hood spokesman confirmed there will be a remembrance ceremony on Wednesday.
Army specialist Ivan Lopez killed three fellow service members with a handgun and wounded 16 others before shooting himself in the head on Wednesday, officials said. It was the second shooting attack on the base in five years following the attack in 2009 when a disgruntled major killed 13 people and wounded 32 others.
Obama has attended similar services after other mass shootings across the country. Before the shooting at Fort Hood, the US President was already scheduled to be in Texas to give a keynote address at a civil rights summit at the University of Texas in Austin on Thursday.