The presence of the Syrian delegation at the London Games starting in July is set to be controversial after more than a year of protests against President Bashar al-Assad's rule led to violence that the United Nations says has killed 9,000 people.
Syrian opposition activists quoted in the British media have urged Britain to ban the head of Syria's National Olympic Committee, General Mowaffak Joumaa, and other officials regarded as close to Assad, from the Olympics.
But Cameron said he did not believe that Syrian athletes should be punished "for the sins of the regime".
"Syrian athletes will be taking part in the Games, and that is right, but let's be absolutely clear: Britain has led efforts within the European Union and elsewhere to institute asset bans, travel freezes and punishing sanctions against this despicable regime and anyone covered by one of those travel bans will not be welcomed in London," he said.
Cameron was speaking at a news conference side by side with Jacques Rogge, president of the International Olympic Committee (IOC), which is making its final inspection of the sporting venues this week before the Games begin.
It was not immediately clear whether any Syrian officials planning to travel to the Olympics are covered by sanctions.
The IOC said this month that Syria would be present at the London Olympics despite the violence in the country.
Pere Miro, an IOC official, said he expected four or five Syrian athletes to qualify for London, mainly in athletics and swimming, and that they would march into the stadium under the Syrian flag. He said Syria was also expected to send four or five officials, with Joumaa among those automatically invited.
Cameron said he and Rogge had discussed security, transport - seen as two of the thorniest potential problems for the London Olympics and Paralympics- and the "legacy" that the Games will leave behind.
London has been a victim of militants in the recent past. In July 2005, four young British Islamists carried out suicide bomb attacks, killing 52 commuters on the capital's transport network, a day after the city was awarded the Games.
Rogge said he was confident London would lay on a great Games "but of course we all know that the proof of the pudding is in the eating".
He praised "positive results" in terms of the continuing benefits the Games will provide in regenerating parts of East London and in new sports venues and said he had "no doubts whatsoever" about transport and security for the games.
Britain has said it will provide up to 13,500 troops to protect the Olympics after increased concern about security after the Arab Spring led it to raise the overall security budget to more than £1 billion.
Cameron said the London Games would be ready on time and on budget.
"This will be the biggest and the most integrated security operation in mainland Britain in our peacetime history," Cameron said, but he added that the security operation would not overshadow the Games.
He said it was time to "tear up any notion" that the Games would leave behind "white elephants" in costly sports facilities that would lie unused after the Olympics. "Six out of the eight venues already have long term futures agreed," he said.