Washington DC's Capitol Police have ordered a review into a BBC report that an armed police team was ordered not to respond to Monday's mass shooting.
A tactical response team from the force was told by a supervisor to leave the scene instead of aiding municipal officers, police sources told the BBC.
The Capitol Police sources suggest they could have saved lives had they been allowed to go in.
Aaron Alexis, 34, killed 12 people at the Washington Navy Yard.
In a statement on Wednesday, the US Capitol Police Board said the force's Chief Kim Dine had asked it to conduct "a comprehensive, independent review of the facts surrounding the Capitol Police's response to the Navy Yard shootings".
The Capitol Police Board said it had responded by establishing a "Fact Review Team", led by Michael Stenger, a former assistant director of the US Secret Service.
'Lives may have been saved'
Alexis, a former Navy reservist, was working as a technical contractor and had a valid pass and security clearance allowing him into the highly secure naval facility in south-east Washington DC.
About 8:15 local time (12:15 GMT), Alexis entered Building 197 at the installation and launched his attack.
Armed with a shotgun and a pistol he took from a guard he had shot, he sprayed bullets down a hallway and fired from a balcony down on to workers in an atrium. He also fired on police officers who stormed the building, and was later killed in the shootout.
Multiple sources in the Capitol Police department, which guards the US Capitol complex, have told the BBC that its highly trained and heavily armed four-man Containment and Emergency Response Team (Cert) was near the Navy Yard when the initial report of an active shooter came in at about 8:20 local time.
The officers, wearing full tactical gear and armed with HK-416 assault weapons, arrived outside Building 197 a few minutes later, an official with knowledge of the incident told the BBC.
According to a Capitol Police source, an officer with the Metropolitan Police Department (MPD), Washington DC's main municipal force, told the Capitol Cert officers they were the only police on the site equipped with long guns, and requested their help stopping the gunman.
When the Capitol Police team radioed their superiors, they were told by a watch commander to leave the scene, the BBC was told.
"I don't think it's a far stretch to say that some lives may have been saved if we were allowed to intervene," a Capitol Police source familiar with the incident told the BBC.
The gunman, Aaron Alexis, was reported killed after 09:00.
Several Capitol Police sources who spoke to the BBC asked to remain anonymous for fear of reprisal.
Capitol Police Officer Jim Konczos, who leads the officers' union, said the Cert police are expert marksmen who train for what are known as active shooter situations.
"Odds are it might have had a different outcome," he said of the shooting and the decision to order the Cert unit to stand down. "It probably could have been neutralised."
'A blind eye'
Capitol Police Chief Dine confirmed in a statement to the BBC that he had ordered a review into his force's response, "specifically our mutual aid efforts".
He said that he had been in "close and constant co-ordination" with other police and law enforcement agencies throughout Monday's incident, and had offered resources.
Chief Dine said he was "deeply saddened" by the shootings.
Senate Sergeant-at-Arms Terry Gainer, who oversees the Capitol Police department, confirmed officials were pulling radio logs from Monday's incident and interviewing the officers involved.
"It's a very serious allegation and inference to indicate that we were on scene and could have helped and were told to leave," he said. "It crushes me if that's the case."
Mr Gainer said that while the department's primary responsibility was to protect the Capitol complex, which houses the US Congress, that mission did not allow it to turn a "blind eye" when asked for help.
A Capitol Police officer, who heard the Cert request over the radio to engage the gunman, reported that colleagues within the department felt frustrated they were told to stand down.
The officer described a culture in which emergency responders are instructed not to extend themselves beyond the Capitol grounds for fear of being disciplined.
"They were relying on our command staff to make the right call," another Capitol Police officer said. "Unfortunately, I don't think that happened in this case."
Gwendolyn Crump, a spokeswoman for the Metropolitan Police Department, which protects the city of Washington DC, said allegations that a Capitol Police Cert team was on scene and later stood down were "not true".
Alexis had carved the messages, "better off this way" and "my ELF weapon", on to the stock of his shotgun, law enforcement sources have told US media.
On Wednesday, Alexis' mother apologised to the victims and said she was bewildered by her son's actions.
"I don't know why he did what he did, and I'll never be able to ask him why," Cathleen Alexis told MSNBC from her home in New York.
"Aaron is now in a place where he can never do harm to anyone, and for that I am glad."
Meanwhile, US Defence Secretary Chuck Hagel acknowledged "there were a lot of red flags" in Alexis' background that had been missed in the security clearance process.
He said he had ordered the Pentagon to conduct a wide-ranging review of the physical security at all US defence installations across the world and of the security clearance process.