Two-year-olds Rhys and Shaun Scott died in Dalgety Bay, Fife, on Saturday morning.
In a statement issued through Police Scotland, the twins’ parents, Mervyn Scott and Sarah Aitken, said: “We would like to thank everyone for their support at this unfortunate and difficult time.”
The couple offered “special thanks to all the medical staff, family, friends, neighbours and the police for their efforts, hard work and time spent helping and trying to revive our miracle babies”. The parents added: “Both boys were long-awaited little soldiers who were full of love, happiness, fun and cheek.
“Individually and together they have touched the lives of everyone they met. We, along with our family and friends, are still in shock and devastated at such a tragic loss from such a ‘freak’ accident. They have been taken from us far too early and will be forever missed and loved.
“We wish to be left alone and be given the privacy needed to grieve.”
The boys were treated by police officers and paramedics at the scene, before being rushed to Victoria Hospital, Kirkcaldy, where they died.
Officers are continuing to support the family.
Inquiries to establish the full circumstances are ongoing.
The scene remained cordoned off with police tape and officers were standing guard at the front of the home yesterday morning. It is understood the pond is in the back garden of the house.
Local MSP Alex Rowley described the incident as “every parent’s worst nightmare”.
He said: “The loss of two young lives from the same family is just heartbreaking. My thoughts and prayers, and those of the whole community, are with the family.”
Dalgety Bay councillor Dave Dempsey said the community was shocked.
He said: “It is enormously sad and my heart goes out to the family.
“I cannot begin to imagine what the family are going through – it is everyone’s worst nightmare. The whole community is shocked. As local councillors, we were all notified that two young children had fallen into a pond and died. To think it is twin boys is heartbreaking.”
Police and ambulance crews were called to the scene.
A Police Scotland spokesman said: “We received a call around 8.20am on Saturday following a report of concern for two children at an address in Dalgety Bay, Fife.
“Two male twins, aged two, had reportedly drowned in a fish pond and officers attended with the Scottish Ambulance Service. The children were taken to the Victoria Hospital in Kirkcaldy where they sadly died.”