A tactical response team of the Capitol Police, a force that guards the US Capitol complex, was told to leave the scene by a supervisor instead of aiding municipal officers.
The Capitol Police department said senior officials were investigating.
Aaron Alexis, 34, killed 12 people at the Washington Navy Yard on Monday.
“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.
A former Navy reservist, Alexis was working as a technical contractor for the Navy and had a valid pass and security clearance allowing him entry to the highly secure building in south-east Washington DC.
He entered the building about 8:15 local time (12:15 GMT) and opened fire. He was later killed by police who stormed the building.