During that first phase from May 12 to June 12, more than half a million of a total three million tickets on offer were snapped up -- double of what was expected -- and organisers hope to make a total of 183 million [US $213.6 million].
A separate batch of 2.3 million tickets has already been snapped up by sponsors of the Games, national Olympic committees, and TV rights holders for an estimated 80 million.
"We have already covered 66 per cent [120.7 million] of our budget and we urge fans to hurry up and buy their tickets so as not to miss the unique opportunity to watch the Games," ATHOC executive director Martin Simitsek told Reuters.
"[This time] the purchase will be done without prior request, with immediate confirmation of the buy if the tickets are available," Simitsek said.
All prior purchases required an initial request, which was processed according to demand.
The second phase is scheduled to run until the end of February, compared to the previous one-month period.
Sources close to the ticket sales have said popular Olympic disciplines, including swimming, diving, and water polo, are already almost sold out, as are the opening and closing ceremonies.
Average ticket prices are about 35, a considerable drop from 53 at the 2000 Sydney Games. More than two-thirds of all tickets cost up to 30.
Spectators from outside the European Union and Iceland, Norway and Liechtenstein will have to purchase their tickets through their country's Olympic committees.
The Games, returning to the site of the modern revival after 108 years, open on August 13, 2004.
Despite years of construction delays and organisation problems that have earned the ATHOC several stern warnings from the International Olympic Committee, they have been successful in their marketing and ticketing programmes.