The two adults killed were identified as Jeffrey and Cynthia Mather, according to Gary Guenther of the Summit County Medical Examiner's Office, who spoke to CNN by phone.
Frank Risko, fire chief for Northfield Center Township, said the children were girls ages 8 and 12.
The fire marshal's office said in a statement that "details of this incident cannot be released at this time" because of the ongoing investigation.
Neighbors heard the explosion at around 8:30 p.m. Monday and ran into the burning home trying to rescue the family. One of the neighbors, Jim Russo, told CNN affiliate WEWS
that he made it as far as the kitchen.
"There was debris and a lot of insulation all over the ground, a lot of smoke," he told WEWS. "And we started screaming to ask if anybody was in there, and nobody responded. We couldn't get upstairs because that was engulfed in flames."
Risko, the fire chief, said the fire was one of the worst he has seen in his 25-year career. The house "was completely engulfed" when firefighters arrived, he said.
By the time the fire was put out, only a fraction of the second floor was intact, Risko said.
Late into their long, grisly night, after battling the fire for several hours, firefighters found the body of one of the children near her mother's, the chief said. The father's body was found on the first floor near the rear of the home, he said.
Risko said his department doesn't often deal with fatal fires.
"It's difficult," he said, his voice breaking.