"We can do better," Cameron acknowledged Monday, after games organizers explained their range of tactics to fill the gaps with ordinary sports fans.
Organizers needed to "make sure more people get to see more games and also that there are fewer empty seats," Cameron told broadcaster ITV in an interview.
Cameron had earlier chaired a meeting of his government's Olympics panel, and expressed confidence that the organizing committee was "on track" to meet his challenge.
Around 3,000 extra tickets were made available late Sunday, and quickly sold, for the following day's events to start meeting public demand, organizing committee spokeswoman Jackie Brock-Doyle said at a briefing.
The empty seats problem has lingered beyond the first weekend of competition, taking some shine off a halo-effect left by Friday's opening ceremony which was hailed with lavish praise from most British people.
Organizers, who long promised packed games venues, were then criticized after blocks of prime seats were unused across the opening weekend — and insisted that sponsors were not to blame.
Seats were left empty mostly by accredited sports and national Olympic officials, athletes, some media, plus "a handful of sponsors." Military personnel resting from onsite security duties and neighbourhood students and teachers were offered tickets while organizers sought to get more fans into the arenas.
Sports governing bodies have been the main source for returning privileged-access tickets.
"We have talked to the international federations," Brock-Doyle said. "Everybody is giving up what they can. We were able to put back into the pot for sale about 3,000 tickets (Sunday) night and they've all been sold."
Around 600 gymnastics were freed up, plus 400 for morning sessions in beach volleyball and 200 more in the evening. Additional space was made for fans to see water polo, handball and equestrian, she said.
Each evening, sports and national Olympics officials will now be asked to give back some tickets for fans to make late buys.
"We are doing it session by session," Brock-Doyle said. "We really are doing the best that we can."
Ticket holders leaving an event are also being asked to "recycle" their ticket by allowing its resale for just a few pounds (dollars) to a potential spectator already cleared by security inside the Olympic Park.
Cameron accepted the efforts being made, and that a perfect solution is unlikely.
"You can never solve the problem completely because there have to be some seats left for the accredited Games family," he said.Suggest a correction