Sergei Mitnik did not apply for release on Sunday when he appeared in a bail court hours after being charged with the murder of an elderly woman inside a unit at Sydney's Bondi Beach.
The woman in her 90s was found with significant stab wounds to her torso about 5.15pm on Saturday. She died at the scene.
Mitnik, who police said knew the woman, was arrested at the home before being charged with domestic violence-related murder.
Defence lawyer Javid Faiz said the event was "extremely serious", adding there were concerns about his client's mental health.
He noted an appointment with a psychologist was cancelled a month ago and his client had been taking the medication Ozempic, which "had an effect on him".
There was no application for bail and the case was adjourned to Thursday.
Hours before the elderly woman's death, a 23-year-old died after being found with stab wounds inside a home in Wagga Wagga, in southwest NSW.
Adam Mark Perrim, 31, was arrested almost nine hours later at another home in the regional city and was later charged with the young woman's murder.
The pair were in a relationship, investigators said.
He briefly appeared before court on Sunday but did not apply for bail.
The 31-year-old will next appear in court on November 18.
Later on Saturday, the body of a 70-year-old woman was found at Mole River in the state's north after reports of a domestic violence incident in the regional district about 9.35pm.
Police believe a 37-year-old man entered a property and tried to steal a vehicle before assaulting a 74-year-old male resident.
The younger man was arrested and police then went on to search the neighbouring property, where they discovered the woman's body.
Part of the house was damaged by fire, police said.
The 37-year-old man has been charged with murder and is due to appear before court on Monday.
Police said he and the woman also knew each other.
Premier Chris Minns said his thoughts were with the families and communities of the three women.
"These are shocking crimes and families are today dealing with unimaginable grief," he said.
NSW Opposition Leader Kellie Sloane said she was horrified by the three women's deaths.
"My thoughts are with their families, friends and communities, and with the police, paramedics and neighbours who responded," she said, adding the incidents could not be treated as "background noise".
Almost one-third of all homicides in Australia are family or domestic violence-related, according to Australian Bureau of Statistics data.
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