Staff Sergeants Bryan Black, Jeremiah Johnson, Dustin Wright, and Sergeant La David T Johnson died and two others were injured when a group of a dozen US Army soldiers and 40 troops from Niger were ambushed on 4 October.
The bureau told the Wall Street Journal it is not uncommon for it to get involved in these types of military investigations and it actually has the authority to take lead on the case, though it has not done so as yet.
The bureau could not be immediately reached for comment.
The Pentagon’s initial assessment was to blame Isis militants.
Congress, however, is questioning not only the purpose of the mission but why the Green Beret-led team was without sufficient support to fight off the 50 Isis militants.
In the ensuing rescue operation to get the US soldiers out of the area during a firefight with the militants, it appears Mr Johnson’s body was left behind.
His body was only recovered 48 hours later - found by Nigerian nationals - and returned the US.
Senator John McCain, a retired Naval officer and Chairman of the Armed Services Committee, said: “We’ve been waiting for weeks and weeks...We will not sit by without having a complete understanding of what’s going on.”
But, he noted, the "US military does not leave its troops behind".
Mr Mattis headed to Capitol Hill on Friday afternoon to meet with Mr McCain, after he threatened to potentially use a subpoena to compel information from the Pentagon and the administration about the Niger attack, complaining that “it was easier under Obama” to find out about active military operations.
White House Chief of Staff John Kelly, a retired Marine General, said that "an investigation doesn’t mean anything was wrong ... doesn’t mean that heads are going to roll."
Mr Kelly said the Defence Department just needs to find out what happened.
Mr Mattis, in response to some news reports, asked that the media "not question the actions of the troops caught in the firefight" who "did everything they could" to recover all the wounded and killed in action at the same time.
"We at the DOD like to know what we’re talking about before we talk," Mr Mattis said as an explanation for the lack of more details on the investigation.
Mr Mattis confirmed that the soldiers were there on a foreign internal defence training mission to "help the people in the region defend themselves."
He said twice that these types of counter-terror missions are done "by, with, and through our allies.”
He also said the media should not "confuse" the need for rapid information with the military's ability to provide it at that rate given the circumstances.
Amid the investigation, Donald Trump has drawn sharp criticism for his public and private handling of these soldiers’ deaths and dealings with their families.
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