Constable Jim Douglas, 50, was having a drink with his brother in the Monaco bar in Lombard Street when one of the gunmen singled him out and opened fire. He was shot twice in the body and once in the head.
A lifeguard drinking in the pub tried to give first aid but Constable Douglas died almost at once.
As the gunman opened fire, at about 3.30pm, staff and customers flung themselves to the ground. The men, wearing baseball caps, fled into streets packed with Saturday shoppers.
They left a suspected bomb in the front doorway of the pub, and the bar was evacuated amid fears that the device was about to explode. Army bomb-disposal experts carried out a controlled explosion on the package before declaring it a hoax.
Police later found a black taxi that had been hijacked and abandoned about a mile from the pub in the west of the city. It is understood that it was used as a getaway vehicle by the terrorists. Police want to interview a person who is believed to have handed one of the terrorists, who was wearing smart casual clothes, his cap after he had dropped it getting into the cab during his escape. The taxi is thought to have been driven by a third terrorist.
The IRA, in a telephone call to a Belfast radio station, claimed responsibility for the attack last night.
Constable Douglas was married with two children, aged 12 and 17. He had served in the Royal Ulster Constabulary for 16 years and worked in a Belfast police station. He lived on the outskirts of the city. An incident room has been set up by the RUC, which is trying to trace witnesses who fled as soon as the shooting started.
The off-duty officer was the second member of the RUC to be murdered in Northern Ireland this year. His killing brought the death toll for the year in the province to 67.