The IRCTC website began booking tickets for travel on special trains after 6 pm, two hours behind the scheduled opening time of 4 pm, and all AC-1 and AC-3 tickets for the Howrah-New Delhi train were sold within the first 10 minutes.
The bookings were slated to open at 4 pm, but got delayed due to a technical glitch.
The Howrah-New Delhi train is scheduled to begin its journey Tuesday from Howrah at 5:05 pm.
As per the ticket availability on the website, all AC-1 and AC-3 tickets for the Bhubaneswar-New Delhi special trains were also sold by 6.30 pm.
Select passenger train services are beginning from May 12, between Delhi and some major cities across the country.
"Special trains are being uploaded in system. Booking will start soon," the IRCTC tweeted at 4.43 pm, explaining the delay.
Sources said the website "did not crash, but data was being uploaded". They had urged passengers to "please wait".