UPDATE: Brandon Lorenz was released from custody Wednesday after prosecutors declined to press charges, according to the Honolulu Star-Advertiser.
The news outlet reported that the victim, Megan Isomura, allegedly posted, "It wasn't Brandon. It wasn't him," to her Facebook page on Tuesday.
The case remains under investigation.
A 34-year-old man turned himself into Honolulu Police on Monday afternoon after a woman and her two young children were found stabbed in their sleep.
Megan Isomura, 28, her 8-year-old daughter and 6-year-old son were found stabbed a total of 16 times early Monday morning in their home at the Kamehameha IV Housing Project. All three victims were taken to Queens Medical Center in serious, but stable condition.
Police searched for the suspect, Brandon Lorenz, through the morning.
Authorities say Lorenz went to the Honolulu Police Department's main station at 4:15 p.m. and was arrested on three counts of attempted murder and one count of burglary.
Honolulu police spokeswoman Michelle Yu told the Honolulu Star-Advertiser that they believe the suspect knew the victims, but would not describe their relationship.
The suspect's home address matches the address of the home where the attack occurred, according to a report from KITV4, and Hawaii News Now is reporting that Lorenz is Isomura's ex-boyfriend, although he is not the father of the children.
Police also told the Honolulu Star-Advertiser that the suspect has been convicted of minor violent crimes in the past, including misdemeanor harassment and assault and abuse of a household member.