Claire Rogers, 13, and her friend Daniel Gibbs, 10, were found in Claire's room by her father, Stephen, at their home in Croxley Green, Hertfordshire, yesterday afternoon.
He cut them down and lay the children on the floor to begin frantic attempts to save their lives.
Both had stopped breathing and paramedics tried to resuscitate them. They were taken to Watford General Hospital, where they were later pronounced dead.
Police described the incident as a tragic accident and emphasised that there was no suggestion of foul play or suicide.
The Bedfordshire and Hertfordshire ambulance service was alerted by a 999 caller who said a child had stopped breathing.
While the caller was given advice over the telephone, three ambulances went to the house, where paramedics found Claire and Daniel, who lived near by.
Mr Rogers had last seen the pair at least two hours before and went upstairs to Claire's bedroom because the family was about to go shopping.
Daniel Gibbs's father, Paul, said last night that his son was a "normal happy-go-lucky kid". "He was a very, very loving child. He wasn't one who was shy of giving you a cuddle."
There was speculation that the children may have watched the bank holiday television film Robin Hood, Prince of Thieves, which showed a number of outlaws being hanged.
However, Detective Inspector Paul Lazell said: "There was no mention of that while we were round there.
"The parents have suffered enough, and I wouldn't like to speculate on that. We have no idea what they had been doing."
He added: "Claire and Daniel were friends playing an innocent game which appears to have gone tragically wrong."Reuse content