Police said they do not yet have an exact motive for the attack.
Seven people remain in hospital, many with "serious or critical injuries".
Police are asking anyone who has had contact with Kinner in recent months to call the department or reach out online at www.343COPS.com. Four were said to have had life-threatening injuries.
The assault occurred at a 3-year-old's birthday party, the Statesman reported.
Kinner had recently been a guest at the complex but was asked to leave Friday over bad behavior.
Boise Police Chief Bill Bones hinted that some victims may be children: "The age range of the victims varies dramatically, and it's affected all aspects of the families within the apartments", he said.
While wearing a tattered off-white sweatshirt with his arms shackled to his waist, Kinner told the judge he didn't understand the charges or proceedings.
Police tape blocks off an area at a Boise, Idaho, apartment complex, Sunday, July 1, 2018, where nine people were stabbed during an attack that targeted a child's birthday party the night before. He was arrested near the scene Saturday and is being held without bond at Ada County Jail.
A knife-wielding stranger turned up at a three year-old's birthday party before stabbing her and other refugee toddlers, police say.
Nine people, including six children, were injured after a man went on a stabbing rampage at an apartment complex housing refugee families Saturday night, police in Boise, Idaho said. In the photo she is standing in front of a Disney Princess-themed banner and gesturing to a pink, doll-shaped birthday cake.
The judge ordered that he be appointed a public defender anyway. For now, cops are only describing Kinner as being from Los Angeles, California, but he was a temporary resident at the Boise complex until he was asked to leave on Friday, they said.
Kinner returned Saturday, when the girl was having her party a few doors down from where he had stayed, according to police.
Suspect Timmy Kinner, 30, appeared in court Monday and faces one count of murder.
"We were on the phone with the police", Esrom said.
The woman who took Kinner in was not harmed and was not at the residence at the time of the attack.
Police said on Monday that one child has been treated and released from hospital. Three adults were wounded trying to stop the assault. It's left many in the community reeling and seeking ways to help. The attack had a devastating effect on the people.
"It is heartbreaking that adults and children who fled the horror of war and conflict to find safety in America had to experience violence all over again", Hans Van de Weerd, vice president of USA programs, said in a statement.