At a news conference, police identified the suspects as Adan Espinosa Canela, 17, and Policarpio Espinosa, 22. They are cousins and are related to the victims although it was not immediately clear in what way.
The children were identified as 9-year-old Ricardo Espinoza; his 9-year-old sister, Lucero Quezada; and their 10-year-old cousin, Alexis Quezada, a boy. One child was beheaded, the other two partially beheaded.
"I've been around for 35 years and I've seen, unfortunately, my share of murders, but I've never seen something as bad as this," Deputy Police Commissioner Kenneth Blackwell said earlier.
Homicide detectives had stopped an unidentified "person of interest" in connection with the crime late Thursday.
The children were found when one of their mothers returned home from work Thursday. The woman, who speaks Spanish but little English, told a neighbor, who called 911.
"There's blood all over my apartment," a woman said in the 911 call, apparently providing translation for the mother. "They've killed my family!"
The first officer on the scene "couldn't handle it" and had to give the call to another officer, Blackwell said. "Walking in on a scene, seeing children of that tender age in that condition, certainly breaks your heart."
Police found a butcher knife they believe was used in the killings near the apartment where the victims were discovered.
Parents and teachers at the children's school, Cross Country Elementary, hugged each other Friday morning and cried. Officials said grief counselors would be on hand to help the 700 students.
The mother gave police information about where to find the man who was questioned, Blackwell said. Officers stopped him a few blocks from the crime scene.
Blackwell said the man's relationship to the children, if any, was not known but he was an acquaintance of the mother.
The art deco apartment complex is on the edge of a neighborhood of well-tended homes. It is largely Orthodox Jewish, with a mix of white, black and Hispanic residents.
Al Johnson, who lives in the complex, said she heard the mother screaming.
"They were very nice, cordial kids," Johnson said. "It's such a shock to everyone. "It's a very quiet, peaceful community."