A man accused of the stabbing murders of two people at a western Sydney unit has been refused bail after appearing in court for the first time over the killings.

Eric George Delaney, who has yet to enter a plea, did not apply for bail and it was formally refused by magistrate Holly Kemp at Liverpool Local Court on Thursday.

The 34-year-old was arrested about 4.15pm on Tuesday, less than 30 minutes after he allegedly murdered Damien Roach and Leah Mumbulla at a unit on Huntley Place in Cartwright.

Mr Roach, 40, was treated by paramedics at the scene but died, while Ms Mumbulla, 34, died at Liverpool Hospital.

Police said it is believed the couple visited the unit to settle an ongoing dispute.

Delaney is scheduled to next appear at Liverpool Local Court via audio-visual link on February 24.

AAP