Of 1.9 million people who applied in the first round, 1.2 million did not get tickets.
Of the first round sale, London 2012 chairman Lord Coe said: “It has been a massive demand which has created huge disappointment.”
The first 10 days of sales in the second round, to July 3 at 6pm, will be open only to people who applied in the original sale, between March 15-April 26, and came away empty-handed.
There will be 2.3 million tickets up for grabs on a first-come first-served basis, with sports fans who missed out in the original sale first in the queue.
Sports fans who got tickets in the first round will get another chance to buy in a second round sale that starts from 6am on July 8 to 6pm on July 17.
Tickets for archery, the athletics race walk, basketball, beach volleyball, boxing, canoe sprint, mountain biking, dressage, football, fencing, handball, hockey, judo, rowing, sailing, synchronised swimming, taekwondo, table tennis, volleyball, wrestling and weightlifting will be on sale, including 44 medal events.
There will be 1.5 million tickets costing £50 or less.