The SRU had to introduce a queuing system on the first day of the sale as the first batch of tickets for the Murrayfield games against England and France became available.
The 10,258 available tickets sold in two hours - a record for the www.scottishrugby.org site, which initially struggled to cope with the number of people logging on.
9,928 tickets were picked up for the Calcutta Cup clash on Saturday 13 March, while 2,505 tickets were sold for Scotland's opening fixture against France on Sunday 7 February.
An SRU spokesman said: "Due to the unprecedented, record level of demand in the opening hours of the online sale, some supporters may have experienced a delay in buying their tickets.
"But we thank them for their perseverance. Ticket sales are progressing apace at present."