Officers went door to door looking for tips that could lead to a suspect or a motive.
"We're working with a blank sheet of paper," police spokeswoman Monique Martin said.
Most of the victims had been shot and at least one child had been stabbed, authorities said. The children ranged from about 1 to 12 years old, police said.
The surviving children were hospitalized, two in very critical condition and the other in serious, according to police. Their families asked that no details of their conditions be released, and it was not clear when or whether they might be able to help investigators.
Meanwhile, authorities hoped for leads from the rough-edged community called Binghampton, where low-income houses and apartments sit near cheap motels and junkyards.
"We know there are people out there who have heard things, seen things, known things" that might help "put together pieces of the puzzle on what occurred in that home," said Lieutenant Joe Scott, a homicide detective.
The street where the killings occurred remained blocked off to bystanders and media yesterday, the home cordoned off by crime-scene tape. A forensics van was parked out front.
It was not clear how the killings could have gone unnoticed - police said five of the six dead were shot - though the neighborhood does experience some drug- and gang-related violence. Early yesterday, as police investigated the six slayings, two men were shot and wounded in an unrelated home invasion about a mile away.
The weekend attack appeared to be the worst single shooting in Memphis in at least 33 years. In May 1973, a man with a history of mental illness randomly shot and killed five people, including a police officer, before police killed him.
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