President Obama's National Security Council has taken control of all the informational briefings on the Fort Hood shooting and ordered that congressional leaders along with the chairmen and top Republicans on the relevant committees receive the briefings first, a key Democratic lawmaker said Tuesday.
White House spokesman Tommy Vietor said "the NSC is playing a coordinating role for briefers -- not taking on all the briefings directly." He added that is a role that NSC would normally play on such issues.
"I have been told that the director of the National Intelligence is still committed to providing the full membership a briefing on the activities within the jurisdiction of this committee," Rep. Silvestre Reyes, D-Texas, chairman of the House Intelligence Committee, said in a written statement.
"I believe that this will occur, and I will push to schedule a briefing before the end of this week," he added.
There was a briefing Tuesday morning for nine lawmakers, including House Speaker Nancy Pelosi, Fox News has learned.
Geoff Morrell, a Pentagon spokesman, said NSC will put together a team that will include representatives from the Army, Department of Defense, FBI, and National Counter-Terrorism Center.
In an interview with Fox News, Reyes said Congress should wait to "find out all of the facts" before launching a full-blown investigation.
But on Tuesday, Rep. Pete Hoekstra, the top Republican on the House Intelligence Committee, sent Pelosi a letter, signed by all Republican members of the panel, requesting an investigation.
"We strongly disagree with the suggestion that Congress should abdicate its Constitutional oversight and fact-finding responsibilities in this regard," the letter read, adding that evidence shows that oversight in no way interferes with an ongoing criminal prosecution.
"The future security of over 300 million Americans is far more pressing than after-the-fact investigation of one man," the letter said.
Meanwhile, the Pentagon is planning to investigate its procedures in the wake of the Fort Hood massacre, a probe that will be taken up either by the Department of Defense or the Army, a Pentagon spokesman told Fox News Tuesday.
Panels would be convened by either the Army or larger Defense Department to conduct a broad examination beyond the particulars of Army psychiatrist Nidal Malik Hasan and into how all the U.S. military services keep a watch on potential problems in their ranks, senior military officials said.
However, Morrell said it's too early to say whether a department-wide panel would supercede an Army investigation, though that is something being considered in the planning process. The possible probes are still in the planning stages.
Defense Secretary Robert Gates wants a unified probe that hits all corners of the Pentagon, Morrell said.
He told Fox News that it's unlikely that both the DoD and the Army would investigate.
"If there are issues larger than one service, it would make sense to have a wider probe of this," he said. "We suspect there are larger issues."
The investigation would consider some questions Morrell described as immediate, although he would not be specific, and some he said will take longer to frame and sort through.
Another official said there will be a fast look at whether the military has missed red flags that might signal there are other potentially dangerous service members out there.
"A tragedy like this certainly gives this institution an opportunity to reflect on whether we are doing everything that we can and should to prevent something like this from happening," said Defense Department spokesman Bryan Whitman. He said Gates has not made any decision on a defense-wide review.
Morrell said there has been no decision on the structure, time line or staffing for a review.
"He's trying to come to a resolution of this as quickly as possible, but this has not been nailed down quite yet," Morrell said of Gates.
Hasan, an Army major, is accused of killing 13 people in the Nov. 5 shooting rampage at the Texas base.
Army Chief of Staff Gen. George Casey had said earlier that the service would take a hard look at itself following the Nov. 5 shooting.
Any new review would be have to be careful not to interfere with the continuing criminal investigation, defense officials said. And so it could look at things outside that realm such as personnel policy and practices and whether there are adequate health services for troubled troops, one official said.
Two military officials said Tuesday that Casey is looking at forming an investigative panel that would consider Hasan's career development and at what point someone should have or might have raised an alarm, one of the officials said.
The proposed Army probe would focus on Hasan's six years at Washington's Walter Reed Medical Center, where he worked as a psychiatrist before he was transferred to Fort Hood in July, an official said.
The doctors who oversaw Hasan's medical training had discussed at a meeting concerns about Hasan's overly zealous religious views and strange behavior months before the attack, a military official told The Associated Press last week. Hasan also was characterized as a mediocre student and lazy worker, but the doctors saw no evidence that he was violent or a threat. The military official spoke on condition of anonymity because the official was not authorized to speak publicly about the meeting.
The FBI learned late last year of Hasan's repeated contact with a radical Muslim cleric in Yemen who encouraged Muslims to kill U.S. troops in Iraq. President Barack Obama already has ordered a review of all intelligence related to Hasan and whether the information was properly shared and acted upon within government agencies.
Fox News' Justin Fishel and Steve Centanni and The Associated Press contributed to this report.