Police spokesman Paul Browne said Thursday that at least two of the younger children had slit throats.
The body of 14-year-old C.J. Jones was found in a separate room. Browne said his throat also was slit and there was a razor under his body.
Browne said the boy recently had been kicked out of a public pool for setting a fire there and that neighbors described him lighting paper on fire in front his apartment building in recent days.
"We believe the fire was intentionally set and our investigation is continuing," Fire Department spokesman Steve Ritea said.
The third-alarm fire broke out inside the home on Nicholas Avenue just before 4:30 a.m.
The blaze started on the second floor and quickly spread. The victims were trapped in the multi-family home and could not escape.
The mother was identified as 32-year-old Lisa Jones. The children were ages 14, 10, 7 and 2. The 7- and 10-year-old children were girls and the other two were boys.
Three other families in the home were able to escape.
Neighbors said Jones attended a beauty school during the day.
"She came out here to try to make a better life for her kids," said her friend Shaquawna Meaders, 25, who lived down the street and was at Jones' apartment Wednesday night.
Jones came from Trinidad; the children's father lived on the island of Jamaica.
"Everywhere she went, if they weren't in school, the kids were always with her," said Meaders, tears streaming down her face.
Officials said they could not find any smoke detectors in the apartment.
"We keep trying to remind people that a simple $10 or $15 smoke detector could have made a difference in saving five lives here," Fire Commissioner Sal Cassano said at a news conference at the fire scene.
Meaders identified the children as 2-year-old Jermaine, 7-year-old Melanie, 10-year-old Brittany and 14-year-old C.J.
Jones' downstairs neighbor, Criseena Lee, who escaped unharmed, also described Jones as a devoted mother.
"She was trying to better her life for her and her children," she said. Jones had lived in the building for about one year and "took care of her kids very well," Lee said.
"The kids were sweet, very innocent," she said. Lee's children, ages 6 and 10, played with Jones' kids, and they went to the pool together, she said.
Meaders described the last evening at her friend's apartment as "a nice night," with C.J. singing and making them all laugh.
Fire officials said the blaze originated in Jones' apartment and quickly move through the attic space and roof.
Assistant Fire Chief Joseph Pfeifer said a firefighter was able to get Jermaine out of the burning apartment because the boy was near the front door. The other children were in the middle of the apartment and the mother was toward the rear, he said. They were pronounced dead at the scene.
Jermaine was taken to a hospital, where he was pronounced dead.
Nicholas Cotton, who lived in the other second-floor apartment with his girlfriend, Shannon Barbach, said they were awakened by banging. He went to the window and saw people outside yelling, "Fire!"
He didn't see anything until he opened his bathroom door and saw flames shooting through the wall from Jones' apartment on the other side.
Cotton's apartment had two exits, but Jones' had only one, he said.
The fire mostly destroyed Jones' apartment and the roof; the facade of the first floor and the part of the second floor where Cotton's apartment was located did not appear to have fire damage.
(The Associated Press contributed to this report)