The suspected burglar was shot and killed after he threatened the officer with a handgun, a police spokeswoman said.
The man is said earlier to have threatened an unarmed officer with the gun.
The incident began at 6.30pm on Thursday when police were called to burglary at a house in Clarendon Street, Bedford.
Armed officers were called in when a man was seen inside the premises with a handgun.
Houses in the area and a nearby swimming pool were evacuated.
"The man appeared at windows with the gun and brandished the weapon several times," said the police spokeswoman.
"He was warned that armed officers were there. He leant out of the first-floor window and pointed the gun at an armed officer. The officer fired his weapon and killed him."
She added: "Police are now trying to identify the man. There will be a full investigation into this."
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