The victims have been identified as Vinh Nguyen, 36, Betty Pham, 36, their 9-year-old son and 4-year-old daughter.
A pile of flowers continues to grow outside the Turing at The Fields apartments where police found the family dead.
They were all found Tuesday following a welfare check.
PREVIOUS REPORT: 2 adults, 2 preteen children found dead in Milpitas apartment, police say
In an update Thursday, Lieutenant Tyler Jamison with the Milpitas Police Department said each family member had one gunshot wound.
"Vinh Nguyen, the father of their two children is believed to be our suspect. A handgun which is legally registered to Vinh was found at the scene," Lt. Jamison said.
A VTA spokesperson confirmed the husband and wife were both employees.
According to a medical examiner's report, the couple was going through a divorce.
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When we went to the apartment complex across the street the from the Great Mall, we met Gary Topenio who knows relatives of the family.
"I couldn't believe it, I was just in shock, I was just like - it can't be, like - I don't really associate something like that bad happens at this time of year. It was like really jarring for me," Topenio said.
Police said the couple had no record of domestic violence-related calls in Milpitas.
Investigators say finding a motive will take time.
"Our detectives are still going through digital evidence and all the evidence they have to determine if there's any notes, any additional evidence that was left from the suspect or any additional information," Lt. Jamison said.
Topenio said his sister lives in the same building and knew Betty Pham and the two children.
"She's really shocked right now. Even though this is supposedly a happy like moment, special time of year, it doesn't erase the fact that if you're struggling mentally - just speak up," Topenio said.
Police said the loss of their lives was preventable and want the public to know that for anyone experiencing distress, help is available.