Organisers said thousands of people have secured tickets since the site opened at 10am today, including places for ceremonies and team sport events.
Tickets will be released in a phased approach over the next three days to manage demand on the dedicated website and phone line.
Problems emerged almost immediately after the final 100,000 tickets for Glasgow 2014 went on sale on Monday last week, with numerous complaints about long delays and issues with finalising transactions.
Sales were temporarily suspended in the early hours of Tuesday morning but, after a second day of problems, Glasgow 2014 suspended all sales until the issues could be fully resolved by Ticketmaster, which is handling the sales.
Organisers said sales appeared to be going smoothly today.
A Glasgow 2014 spokesman said: "We're delighted with the enthusiasm of customers visiting the ticketing website and hotline since opening this morning.
"While it's been busy, there are currently no queues and there are thousands of customers who have been successfully securing tickets. We've also been seeing lots of positive feedback on social channels.
"We thank everyone for their support so far. While there are still lots of great opportunities to be part of the Games, tickets are selling fast so don't leave it too late to buy, especially if you have specific events or days you want to be part of."
Last week it emerged that some fans who called the dedicated phone line were charged while listening to an engaged tone, with some customers running up bills of more than £100.
The phone line that will be used from today will be a free number and all purchases will be posted free of charge, removing a previous £4.50 charge.
Glasgow 2014 chief executive David Grevemberg said today that the system had been tested and retested ahead of the start of the resale, but warned people that "high demand" meant they could still face queues.
Mr Grevemberg told BBC Radio Scotland's Good Morning Scotland: "The original problems experienced last week were intermittent issues that didn't affect everyone.
"It really wasn't one root cause, we had long queues, we had some transactional challenges, but Ticketmaster has undertaken a full, complete review of the system.
"They have checked, tested, retested the system and are very confident now that customers are going to have a much, much better experience.
"Really, we're now focused on selling those tickets and ensuring everyone who wants to be a part of the Games can be a part of the Games."
He refused to say if Games bosses were seeking compensation from Ticketmaster for the problems.
"Right now our main focus has just been working closely with Ticketmaster to address these issues," Mr Grevemberg said.
"Obviously we have a contract with Ticketmaster and we will be looking to that contract. But our focus has really been about getting these tickets back on sale.
"This has been one of our priorities over the last week, since these challenges. But working very closely with Ticketmaster, I'm confident that we've taken the steps necessary to give people a better experience.
"We're very confident that today and tomorrow and Friday, as we start the phased release of these tickets, that we will start to get these tickets sold and we're very excited."
Remaining seats at the opening and closing ceremonies went on sale this morning, along with tickets to watch team sports such as hockey, netball and rugby sevens.
Tomorrow, athletics, badminton, squash and table tennis will go on sale, alongside any unsold tickets from today's release, and all remaining tickets for weightlifting, bowls, rhythmic gymnastics, shooting, boxing, judo and wrestling will be available from Friday.
Diving, swimming, cycling, gymnastics and triathlon are already sold out, Glasgow 2014 said.
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.
Details on how to purchase the tickets can be found at www.glasgow2014.com.