Organisers struggled to count the pairs – who turned up to a designated sports stadium in the thousands – and were unable to meet the strict registration guidelines set by Guinness World Records.
Huge queues built up around the stadium in Colombo as the pairs waited to get their birth certificates checked, and many appeared to leave before they could be added to the registration records.
The guidelines required all the pairs to remain in the stadium to pose for a mandatory group photo or wait at least five minutes in order for the record to be made.
Wasana Ranasinghe, spokeswoman for campaign group Sri Lanka Twins, told AFP: “We had more than we expected. Getting them all to go through a single entry point was not easy.”
Ms Ranasinghe said organisers were able to register just over 6,000 pairs, from the ages of three months to 89 years, during a five-hour period.
“We will know in two weeks if we actually qualified for the record or not, but even otherwise, we have managed to raise awareness,” she added.
Many pairs made long journeys to be at the gathering, some reportedly travelling up to 10 hours by train.
Raheen Usman, a 19-year-old from Colombo who attended the event with her twin Farheen, told Reuters: "It's fascinating. I have made a lot of new friends – all my friends are twins now."
The previous world record was set by Taiwan in 1999, where 3,961 pairs of twins, 37 sets of triplets and four sets of quadruplets gathered.
If the current attempt does not succeed, organisers and other participants vowed to double down and try again next time.
Sri Lanka Twins said it organised the event to raise awareness of underprivileged twins, triplets and quadruplets born into poorer families who struggle to cope.