The figure is almost double the number of calls in the same period last year, and thousands more are flooding in over the new year period.
Bosses said the service is facing “exceptional” demand, with lots of people around the country suffering cold and flu symptoms.
The Sunday Post reported that NHS 24 centres in Aberdeen, Cardonald, Clydebank and South Queensferry have been inundated with calls from patients suffering from those symptoms, as well as stomach bugs.
The bases are expecting to take at least another 29,000 calls over the Hogmanay and new year period.
Confirming the figures, an NHS 24 spokeswoman said: “Already this weekend our call demand on Saturday was over 13,000 calls and by 10.30am on Sunday we had almost 3,500 calls.
“There are lots of cold and flu symptoms circulating and the demand this year has been exceptional.
“For the four-day festive period it was the highest since NHS 24 began 15 years ago and we expect the next few days to be just as busy. Usually January 2 is our busiest day.”
Bosses at NHS 24 said they started preparing for the winter surge several months ago.
Medical director Dr Laura Ryan said: “NHS 24 began its winter planning early in the summer and has worked closely with all of our partners to ensure we could deliver safe and effective care over this very busy time of year.
“This year we have had exceptionally high call demand and I would thank our staff, along with many others across NHS Scotland services, who have already worked very hard to support many thousands of people and will continue to do so over the coming days.”
The figures emerged after doctors at Scotland’s largest health authority urged people with cold and flu symptoms not to visit patients in hospital.
NHS Greater Glasgow and Clyde chiefs said on Friday that those who have experienced flu symptoms in the last 48 hours should not visit patients who are already unwell.