President Barack Obama asked Congress to resist turning the tragic shootings at Fort Hood into a "political theater."
Mr. Obama said he has ordered a review of all intelligence relating to Maj. Nidal Malik Hasan, the Army psychiatrist who is charged in the shootings, and whether the information was properly shared and acted upon within government agencies.
Thirteen people died and 29 were wounded in the rampage.
Some lawmakers have announced they want their own investigations.
Michigan Rep. Peter Hoekstra, the top Republican on the House Intelligence Committee, called for a full examination of what agencies knew about Hasan's contacts with a radical Muslim cleric in Yemen and others of concern to the U.S.
Hoekstra confirmed this week that government officials knew of about 10 to 20 e-mails between Hasan and the radical imam, beginning in December 2008.
A joint terrorism task force overseen by the FBI learned late last year of Hasan's repeated contact with the cleric, who encouraged Muslims to kill U.S. troops in Iraq. The FBI said the task force did not refer early information about Hasan to superiors because it concluded he wasn't linked to terrorism.
Republican Rep. Howard McKeon said he wanted to go ahead with an investigation from the House Armed Services Committee, where he is the top Republican. He said he wanted an investigation that wouldn't compromise law enforcement or military investigations that were continuing on separate tracks.
In the Senate, Sen. Joe Lieberman, a Connecticut independent, said his Homeland Security Committee was opening an investigation.
On Saturday Mr. Obama pleaded for lawmakers to "resist the temptation to turn this tragic event into the political theater." He said those who died on the nation's largest Army post deserve justice, not political stagecraft.
In a video and Internet address released by the White House while the president was flying to the APEC meeting in Singapore, President Obama said he has ordered military and intelligence leaders to undertake a full review of events leading up to the shootings, as well as the motives of the accused gunman, including his views and contacts.
"I am confident that justice will be done, and I will insist that the full story be told. That is paramount, and I won't compromise that investigation today by discussing the details of this case. But given the potential warning signs that may have been known prior to these shootings, we must uncover what steps - if any - could have been taken to avert this tragedy."
"The purpose of this review is clear: We must compile every piece of information that was known about the gunman, and we must learn what was done with that information. Once we have those facts, we must act upon them. If there was a failure to take appropriate action before the shootings, there must be accountability. Beyond that - and most importantly - we must quickly and thoroughly evaluate and address any flaws in the system, so that we can prevent a similar breach from happening again. Our government must be able to act swiftly and surely when it has threatening information. And our troops must have the security that they deserve.
"I know there will also be inquiries by Congress, and there should. But all of us should resist the temptation to turn this tragic event into the political theater that sometimes dominates the discussion here in Washington. The stakes are far too high."
Hasan, 39, was charged on Thursday with 13 counts of premeditated murder, and may face additional charges. Army investigators say he is the only suspect.