There are around 50,000 Olympic tickets up for grabs for events including hockey, athletics and volleyball.
Tickets are generally in the highest price categories — nearly all the cut-price family deals are gone as competitions reach their conclusion.
Games chiefs said they are delighted that such a small proportion of the six million-plus seats remain.
With chances running out to see the Olympics, Games chiefs advise the public instead to focus their efforts on the Paralympics which start at the end of the month.
About 500,000 of the 2.5 million Paralympics tickets remain, including day passes to watch several events at the Olympic park and Excel.
For the Olympics, there are no sales on the day at venue box offices —these booths are being used only for the collection of tickets already purchased. The potential for huge queues for on-the-day sales at the Olympic park forced organisers to adopt this approach.
Thousands more tickets become available each day as organisers reclaim seats in accredited areas given up by media, the IOC and international sports federations.
Some 11,000 accredited seats were snapped up overnight but as these offered some of the best views, many were in the highest-priced A and B categories.
The chances of snapping up athletics returns are limited as up to two million people a day are visiting Locog’s sales website.