Nathshay Yvonne Ward, 33, was charged with capital murder Friday in connection with the deaths of her son and two daughters. She was being held without bail.
Officers found the bodies of Shanieka Y. Ward, 11; Latricia Ward, 9; and Christopher O. Ward, 8, on the floor in three bedrooms Friday, police spokesman Wendell Johnson said.
Officials said the children had been dead for at least several days.
Investigators would not elaborate Saturday on the details of Ward's confession.
When the children were found, "they did appear malnourished," Johnson said.
Johnson said relatives told police they had been trying to visit the family for weeks but Ward would not open the door. Officials said utilities in the apartment had been turned off since Jan. 12, and managers of the apartment complex had been preparing to evict the family.
Johnson said the children had not attended school since the holiday break. Workers with the Alabama Department of Human Resources had tried to visit the apartment in December but Ward refused to let them in, he said.
Ward was single and "took care of her kids," said Leetha McCaulley, who managed the apartment complex until October.
After her car broke down last year, Ward "used to walk the kids to school every day," McCaulley said.
"It was just her and those kids," she said. "She was quiet. Paid her rent on time."