On Monday, Mr. Alexis entered the navy yard, a secure military facility near the Capitol, killing at least 12 people before he was fatally shot by the authorities. The police say Mr. Alexis, 34, acted alone. On Tuesday, the authorities said it had taken only two minutes for officers armed with AR-15s to arrive at the navy yard once they received the first of many 911 emergency calls, but that some officers had mistakenly gone to other buildings inside the property because callers had given various locations for the gunman.

Chief Cathy Lanier of the Washington Police said that law enforcement officers from various agencies exchanged fire with Mr. Alexis. She said the shooting lasted more than 30 minutes.

The authorities said that while they originally believed that Mr. Alexis had been armed with an AR-15, they now believed he entered the navy yard with only a shotgun and may have obtained a pistol once inside. The shotgun had been bought legally in Virginia, said Valerie Parlave, assistant director of the Federal Bureau of Investigation’s Washington office.

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