Speaking during a visit to a West Midlands Police command and control centre in Edgbaston, Birmingham, Mr Cameron described the deaths as "truly dreadful".
Asked what he would say to the victims' families, the Prime Minister replied: "They have my deepest condolences. I think everyone in the country is going to be thinking about them and their families and what happened."
Mr Cameron added: "It was a truly dreadful incident and I know that the police here in Birmingham, here in the West Midlands, are working night and day to get to the bottom of what happened and bring the perpetrators to justice.
"We rely on the police to keep our communities, to keep our country, to keep our shops and homes safe.
"They need our support in doing that job."
Mr Cameron was visiting Birmingham after the deaths of three men, named by their grieving families as 21-year-old Haroon Jahan and brothers Shazad Ali, 30, and Abdul Musavir, 31.
The friends were struck by a car in Dudley Road, Winson Green, Birmingham, as they attempted to protect a petrol station and nearby stores.
West Midlands Police has made more than 300 arrests during disturbances over the past two nights and is questioning a 32-year-old on suspicion of murdering the men.
Giving his general views on the situation facing police across the country, Mr Cameron said: "What they are doing is surging the police numbers on to the streets in places like Birmingham,
"They do need to use robust tactics because most of the people we have seen on the streets are not protesters - they are looters, they are thieves, they are robbers - they are committing criminal acts.
"They need to be arrested, they need to be convicted and they need to be imprisoned. That's what needs to happen."
Mr Cameron went on: "I think we should be clear about what we have seen on the streets in recent days - it isn't protests, it isn't some sort of half-justified attack on this idea or that idea - it has simply been looting, criminal damage, thieving.
"It needs the strongest possible intervention from the police, which is now happening. I welcome that and that's how to bring this to an end."
Those killed in Winson Green were part of a group of around 80 people guarding shops at 1am today.
After their deaths, it emerged that Tariq Jahan attempted to revive his son after running to the scene from his nearby home as the car sped away.
Mr Jahan, who lives about 40 yards from the scene of the incident, told BBC Radio 5 live: "All the street were out and basically he was looking out for the whole community.
"I didn't see it (the fatal incident) with my own eyes. I was round the corner... I heard the car coming at high speed.
"Then we heard the bang and I heard the commotion with the people. I ran towards the commotion and the first guy I found was someone I didn't know.
"I started giving him CPR until somebody pointed out that the guy behind me was my son on the floor.
"Then I swapped positions and started giving him CPR."
Asked to describe his son, who was a keen amateur boxer, Mr Jahan said: "He was a good lad. He was very, very intelligent, very smart.
"He was a good, gifted kid."
Mr Jahan went on: "You can't explain losing a son. It's going to be hard for me now."
The grieving father also appealed for there to be no revenge for his son's death and for the law to be allowed to take its course.
"Tensions are already high in the area. It's already bad enough what we are seeing on the streets now without other people taking the law into their own hands," he said.
The other victims were named by family members as brothers Shazad Ali and Abdul Musavir.
The father of the brothers, who owned and worked at a car wash, was too upset to speak to the media at his home in a cul-de-sac in Winson Green.
But a family friend said Shazad, 30, and Abdul, 31, were simply standing up for what they believed was right.
The friend, who asked not to be named, said: "They were very kind and very friendly and very charming - and they were very caring people as well.
"They were protecting other people's property because the day before the Jet petrol station had been robbed and they (looters) were planning to do it again."
The family friend said Shazad, who had a degree in business management from the University of Central England, was standing near the petrol station with his brother when they were hit.
Appealing on behalf of the family for people not to take the law into their own hands, the man told the Press Association: "It's really, really sad.
"The family just want justice to be done."
West Midlands Ambulance Service said two of the victims were pronounced dead at the scene and the third died today in City Hospital.
Meanwhile, West Midlands Police chief constable Chris Sims called for calm from members of all communities after confirming that his force has made 303 arrests over the past two nights.
Giving details of the incident in Winson Green, Mr Sims said: "Shortly after one o'clock, a group of males has been gathered near to a petrol station on the Dudley Road.
"We believe that they were predominantly Asian males.
"At some point, and in circumstances that as yet I can't fully explain, a vehicle has been driven into that group of males, which tragically has led to three of those men losing their lives.
"Again, those victims come from the Asian Muslim community of Birmingham."
Referring to the 32-year-old man who is in police custody, Mr Sims added: "He has been arrested for murder because the information that we have at the moment would support the idea that the car was deliberately driven.
"You will understand that that is now a complicated investigation that has begun and will continue until we get to the full truth of exactly what has gone on."
Urging everyone in the West Midlands to act calmly, he said: "Like everyone else in Birmingham, my concern now will be that that single incident doesn't lead to a much wider and more general level of distrust, and even worse, violence, between different communities.
"If we are calm, I'm absolutely confident that the people of the West Midlands can get through this ... and that we can rebuild trust between communities."
Speaking to the media outside the hospital, eyewitnesses estimated that the car was travelling at up to 50mph when it hit the men.
Police remained at the scene tonight, conducting forensic inquiries at the petrol station and using a patrol car to conduct tests related to the investigation.
Witness Mohammed Shakiel said the car sped off after striking the men, who he knew by name.
The 34-year-old carpenter said: "We got a call that there had been a car that had been set alight and a group of youths had moved further up the road.
"They put the fire out but there were still yobs on the street - they had no agenda other than simple stealing."
He added that several cars then drove past the group guarding shops, and the occupants shouted abuse before one vehicle returned and mounted the pavement at "tremendous speed" and hit the men, throwing them into the air.
Mr Shakiel said of the victims: "They lost their lives for other people, doing the job of the police.
"They weren't standing outside a mosque, a temple, a synagogue or a church - they were standing outside shops where everybody goes.
"They were protecting the community as a whole."
PA
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