The mother of the children rescued after 40 days in the Amazon jungle told them to leave and find help as she lay dying.
Magdalena Mucutuy survived for four days after the plane crash, Manuel Ranoque, the children's father, said.
Mr Ranoque said his eldest daughter told him their mother urged them to "get out" and save themselves.
The siblings, aged 13, nine, five, and one, were rescued and airlifted out of the jungle on Friday.
"The one thing that [13-year-old Lesly] has cleared up for me is that, in fact, her mother was alive for four days," Mr Ranoque told reporters outside the hospital.
More details have been emerging about the children's time in the jungle and their miraculous rescue - including the first things the children said when they were found.
Nicolas Ordonez Gomes, a member of the search and rescue crew, recalled the moment they discovered the children.
"The eldest daughter, Lesly, with the little one in her arms, ran towards me. Lesly said: 'I'm hungry,'" he told public broadcast channel RTVC.
"One of the two boys was lying down. He got up and said to me: 'My mum is dead.'". He said rescuers responded with "positive words, saying that we were friends, that we were sent by the family".
Mr Ordonez Gomes said the boy replied: "I want some bread and sausage."
In new footage released on Sunday of the children's rescue, the four siblings appeared to be emaciated from the weeks they spent fending for themselves in the wilderness.
Ms Mucutuy and her children had been travelling on the Cessna 206 aircraft to Araracuara, in Amazonas province, to San José del Guaviare, on 1 May when it issued a mayday alert due to engine failure.
She and two pilots were killed when it crashed. Their bodies were found at the crash site by the army, but it appeared that the children had escaped the wreckage and wandered into the rainforest to find help.
The missing children became the focus of a huge rescue operation involving dozens of soldiers and local people.
Rescuers tracked the children down after spotting signs in the jungle, including footprints and fruit that had been bitten into.
Members of the children's community had hoped that their knowledge of fruits and jungle survival skills would give them a better chance of remaining alive.