"The Army has its investigators, the FBI is investigating, and, Bob, the truth will come out," Skelton told CBS News chief Washington correspondent Bob Schieffer. "Let's give them a few days to find out just where the ball was dropped if that's the case."
However, if he's not pleased with what the respective investigatory agencies do, Skelton said his committee would look into the shooting.
"I'm going to wait and see what they do," Skelton said. "If they are not thorough, we will, of course, have additional hearings, briefings on this. It's a tragedy of the first order. It's a tragedy not just for the soldiers and their families that were there. It's a tragedy for all of the families that wear the uniform."
Special Section: Tragedy at Fort Hood
Rhode Island Sen. Jack Reed, who sits on the Senate Armed Services Committee, echoed his fellow Democrat's caution.
"We do have to look closely at what the Army has done, what the whole armed services has done," Reed said. "But Chairman Skeleton has put it in the right context. We have to wait for their careful deliberations. There's a criminal investigation going on."
Reed added that the tragedy at Fort Hood opens up "broader issues" about U.S. troops and their psychological treatment.
"We have to look at the broader issues, not just this incident, but are we taking adequate care of these soldiers?" Reed asked. "Are we providing the adequate support systems for the families? … These are issues that go beyond this incident and responsible for the Congress to look at them."
Skelton linked the shooting to the health care reform bill the House narrowly passed late Saturday night, saying that the bill increased mental health providers for military families.
Another member of the Armed Services Committee, Sen. Lindsey Graham, R-S.C., agreed.
"We've put more medical personnel on the front lines of evaluating people," Graham said.
He added that jumping to conclusions about suspected shooter, Army psychologist Maj. Nidal Malik Hasan, could be dangerous. It's been reported that Hasan .
"Every soldier who shows discontent with the war and every soldier that has a bad performance report - what are we going to do with those folks?" Graham asked. "So, at the end of the day, let's see what the evidence trail suggests here and not overreact because we live in a free and open society. You can be in the military and disagree with policy."
Authorities accuse Hasan of killing 13 and wounding 29 others in the worst mass shooting at a military facility in the United States.
"At the end of the day, maybe this is just about him," Graham said about Hasan. "It's certainly not about his religion, Islam. It's not about the Army; it's not about the war. At the end of the day, I think it's going to be about him."
Reports have also said that Hasan was .
"Do you think the fact that he was a Muslim may have caused the military to kind of step back and be reluctant to challenge him on some of this stuff for fear that they'd be accused of discrimination or something like that?" Schieffer asked.
"Don't take this to a level that we should not," Graham said. "Don't accuse people of basically giving him a pass because he's a Muslim because I don't think there's any evidence of that."
"This is not about theology," Reed said. "This is about doing your duty as a soldier, and also I think we have to be careful not to leap beyond the current investigation."