Home secretary Theresa May insisted that law and order agencies will do all that was necessary to ensure a trouble-free Olympics. London witnessed considerable violence over the last three days, including in Hackney, which is one of the five boroughs in which the Olympics will be held.
May said security plans for the Olympics will be reviewed. Thousands of athletes and hundreds of thousands of people from abroad are expected to arrive in London for the mega sport event, putting pressure on security agencies.
May told the BBC: "We take the issues around the Olympics very seriously. An awful lot of work has already gone into planning in relation to the security and public order in relation to the Olympics and we will continue to monitor that and continue to look at what is necessary and what we need.
On its part, the International Olympics Committee (IOC) said it had ''complete confidence'' in London's ability to hold the event safely.
An IOC spokesman said security is a top priority but that it was not its direct responsibility.
"That is something for the authorities in London in whom we have complete confidence," he said.
"People should be in no doubt that we'll do everything necessary to restore order to British streets, and to make them safe for the law abiding," Cameron said making a statement after chairing a meeting of government's emergency response committee.
"And I have this very clear message to those people who are responsible for this wrongdoing and criminality: you will feel the full force of the law and if you are old enough to commit these crimes you are old enough to face punishment".
The West Midlands Police were dealing with sporadic disorder in Wolverhampton, while youths had smashed shop windows and set cars alight in nearby West Bromwich.
Riot police were also surrounding Birmingham's Mailbox high-end shopping building.
The Prime Minister termed the scenes witnessed on the streets of London and elsewhere as "appalling" and driven by "criminality" and admitted that more police presence and more robust police action was required.
The Greater Manchester Police were involved in a standoff with 70 to 80 young people in Salford, where a building was set alight, while a Miss Selfridge store was reportedly set on fire in the Manchester city centre.
Cameron will chair another meeting of the government's emergency committee at 9 am on Wednesday to review the situation developing overnight, Downing Street said.
Rioting and looting that started on Saturday, sparked by Thursday night's death of Duggan, spread across London, and also flared up in the central city of Birmingham, the western city of Bristol and the northwestern city of Liverpool.
Another person, who was shot in his car during last night's rioting in Croydon died after being admitted to hospital, police said. He was discovered in a car suffering from gunshot wounds at about 9.15 pm as trouble flared in the area.