Derek Connell could face the death penalty for killing his mother, Kim Higginbotham, and her American husband, Christopher.
The couple, both 48, were found dead at their home in Bakersfield, California, on 30 April.
Connell, 29, originally from Shawlands, Glasgow, confessed to the killings during a preliminary court hearing this week.
However, his lawyer Paul Cadman said there was no evidence of premeditation or malice on his part and argued he should be tried for second-degree murder or voluntary manslaughter.
Kern County Superior Court Judge Thomas C Clark turned down his request and said his statements showed “a fair amount” of thought and planning after the killings. Connell has said he used bleach in an effort to clean up blood pooled around the bodies.
Mr Cadman said the killings were a result of post traumatic stress disorder and drug addiction which Connell suffered after serving with the US Army in Iraq and Afghanistan.
During an interview played to the court Connell said: “I had to have done it. There was no-one else in the house.”
Connell said he spent the evening drinking heavily, then returned to his parents’ home. He began living with them after serving a nine-month jail sentence for drink driving in Colorado.
He told investigators he spoke with his stepfather briefly before going to bed. They didn’t argue, and he said he got along well with both his mother and stepfather.
Connell said the next thing he recalled was finding their bodies. He cried as he described lying next to his mother’s body and telling her he was sorry.
Two shotguns, five handguns and seven rifles were seized from the home. Connell said the weapons belonged to his stepfather.
Connell was born in Rutherglen Maternity and lived with his mother in Glasgow’s south side as a child. Kim worked as a secretary and met her future husband while he was stationed with the US Navy in Scotland.
The next hearing is scheduled for next month.