The Cook County Medical Examiner neither confirmed the number of victims nor their identities Sunday.
Authorities say the youngest victim was a 3-day-old baby.
Cicero officials say it was the most deadly fire the town had seen in almost 25 years.
Crews boarded up the house Sunday night to keep it safe until investigators return Monday. The cause of the fire has not been determined.
The blaze broke out early Sunday in a multi-unit apartment building. Authorities say they believed it started in the rear of the building.
Five of the victims died in the rear attack. Two others were recovered in the rear patio, apparently trying to escape.
"It's tremendous. It's something you can never imagine. It's just one of those things you go like, 'Wow,'" said family member Patrick Lewis.
Lewis is among the devastated struggling to make sense of the blaze that he says claimed the lives of five of his relatives.
Sallie Gist, 18, had just returned home from the hospital with her newborn, Byron, yesterday. They were killed along with her 3-year-old son, Rashon, and the baby's 19-year-old father, Byron Reed. Twins Elijah and Aleshia Gist, 16, who were Sallie Gist's siblings, also died, as did the mother's friend, Tierra Davidson, 19.
They all had planned to celebrate Sallie's father's birthday Sunday. He helped others escape from the second floor of the building, but he told ABC7 Chicago by telephone that he was unable to get up to the attic.
"I've been with this family for over 20 years. I've been working with them, and they called me and told me there was a fire," said Cheryl Anderson, a family friend of the victims.
The first calls for help came around 6:30 a.m. Sunday after Cicero resident Victoria Luna saw smoke coming from the three-flat where her mother also lives.
"When I looked down, I saw the back part of her building engulfed in flames," Luna said.
Some 60 firefighters from a half-dozen fire departments responded to the 211 extra-alarm blaze that raged through the residence. They say they were unable to reach the attic in time.
"Our command unit went in, opened up the door, there was a lot of heat, fire, and a lot of smoke," said Ron Opalecky of the Cicero Fire Dept.
In all, 30 people were inside the building when the fire broke out. Cicero officials say they are investigating whether the exits were up to code.
"They're still looking for relatives and friends. We don't know their status," said Ray Hanania, town of Cicero spokesman. "We're going to be looking very closely at the building to determine why seven people couldn't get out of the building."
Close to two dozen people from the residence were taken to a shelter at the town's public safety office where they were expected to get food and emergency care, as investigators try to figure out if the cause of the fire was accidental or suspicious.
Cicero officials say the fire spread to an adjacent coach house.
They also said three firefighters were injured, one more seriously than the other two because part of a chimney fell on him. ABC7 is told he was in stable condition Sunday night.ABC7 Chicago contacted the building's landlord, but that person declined to answer any questions.