"The situation these officers were confronted with was critical - a matter of life and death - three armed men, wearing what appeared to be suicide belts, had already attacked and killed members of the public and had to be stopped immediately," Rowley said.
"As the officers confronted the terrorists - and were shot - a member of the public also suffered gunshot wounds.
"Although we do not believe the injuries to critical in nature, they are in hospital receiving medical attention. We will of course keep you updated on that."
Eyewitnesses had also reported police smashing the windows and trying to get into a pub as the attack was carried out.
"[The police] fired at least 20 times. One of the guys in the pub took a bullet," an eyewitness told The Sun.
Asst Commissioner Rowley said police were making "significant progress" and had found the white van was hired shortly before the attack.
Canada's Prime Minister Justin Trudeau says one of those killed in the London Bridge attack was a Canadian citizen. Thirty-six people remain in hospital with 21 in a critical condition.
A witness to the aftermath of the London Bridge terror attack has told of his horror and fear at the chaotic scenes unfolding outside his home on Saturday night.
Norwegian man Peter Cassizzi, 41, has lived near Borough Market since February and said he was at home with his girlfriend when the sudden silence in his usually busy neighbourhood piqued his attention.
"All of a sudden it went silent. Moments later police in riot gear were storming in and taking up positions," he told news.com.au
"Police were nervous. They seemed like they didn't have a good overview of the situation."
After nearly an hour had passed he went downstairs to assess the situation and said he was immediately confronted by armed police on the hunt for attackers.
"As soon as I stuck my head out the door they yelled at me, get my hands up," he said.
He joined a stream of people coming out of a nearby restaurant and was told to run across London Bridge.
Speaking on Sunday morning from outside the cordon having had no sleep, he said one factor playing on his mind is the sound of shots being fired when he spoke to his girlfriend on the phone around 5:30am.
"That's the thing that's been bothering me about it," he said. "She's terrified, I really want to get back."