Sales were suspended for a second time yesterday amid delays of more than 30 hours and problems with finalising transactions.
Glasgow 2014 chief executive David Grevemberg apologised "unreservedly" to people affected and said the site and phone line would not reopen until the problem is fixed.
A spokeswoman today said Glasgow 2014 would be "in a position in coming days to advise when ticket sales will be back up and running".
An extra 100,000 tickets across all 17 sports and the opening and closing ceremonies went on sale on Monday, but problems quickly developed with people facing long delays and issues with finalising transactions. Around 55,000 tickets have so far been sold, organisers said.
The site was initially closed for an hour yesterday morning to allow technicians to investigate the problem but they failed to resolve it, resulting in a second day of delays and frustrations for sports fans hoping to secure tickets for the Games.
Ticketmaster, which operates the website, was told to close it last night along with the call centre set up to handle sales.
The Glasgow 2014 spokeswoman said they are "urgently reviewing the performance of the ticketing website" today.
"Once this review is complete and any measures have been implemented and tested we will be in a position in coming days to advise when ticket sales will be back up and running," she added.
"It is our absolute priority to be able to meet, as soon as possible, the enthusiasm and demand that sports fans have shown for the final sprint for tickets and we thank all of our supporters and customers for their patience."
Many people took to Twitter to express their frustrations at the system.
Hannah Fitzgerald wrote: "Spent two entire days waiting in the website 'queue' for @Glasgow2014 Commonwealth Games tickets - now today the ticketing site is down !!?"
Olly Bethell tweeted: "Amazed that the Commonwealth Games haven't learnt from the problems around tickets at the Olympics - high demand is a positive though."
Some people waited throughout the problems on Monday and Tuesday to secure tickets.
Pauline Lynch tweeted: "You might not believe me but it took me 31 hours of queuing to secure commonwealth tickets. 31 hours."
About 2.3 million applications were made for the initial one million tickets released last year, with athletics, aquatics and cycling proving the most popular events.