Authorities said the youngsters were aged seven, 10 and 15. According to reports, the eldest child said the boy, thought to be nine-years-old, had been dead for a year and was in the next room.
He also said his parents had not lived in the flat for several months.
The children have been taken to hospital for treatment. They were said to be malnourished and showing signs of physical injury.
A statement on the police department’s website said: “Deputies responded to the apartment at 3530 Green Crest and discovered the skeletal remains of a small child which appeared consistent with the age provided by the 15-year-old.”
The children’s mother and her boyfriend were said to have been located and were being interviewed by homicide investigators.
The children were discovered during a welfare check at the flat, according to NBC News.
Sheriff Ed Gonzales said they may have been in the apartment for month or even a year.
“I haven’t been told they were necessarily locked in, but at that age, it appears they were basically fending for each other,” he said.
The cause of the death of the fourth child, who police said could be the sibling of the other three, is unknown.
Speaking at a press conference on Sunday, Sheriff Gonzalez called the case “horrific” and “very tragic”.
“I’ve been in this business a long time and I had never heard of a scenario like this. It really caught me by surprise,” he said.
“It seems that they were in there while the body was deteriorating,” he said.
“It appears that the remains had been there for an extended period of time. And I emphasize extended,” Sheriff Gonzalez added.
Neighbours expressed shock and disbelief when they learned about the children. Kayla Williams told the Houston Chronicle that she has two children, but she does not plan to tell them what happened.
“I don’t need to put this in their heads,” she said. “This is crazy.”
