A baby found dead in a rubbish bin in San Diego has been named as three-week-old Eliza Delacruz.

San Diego police said a homeless man discovered the baby face down inside a garbage bag while rummaging through the bin behind a restaurant in Palm Drive, Imperial Beach.

The search for the missing baby was launched after a gunman took her from her Long Beach home after shooting at her parents and her uncle. The mother and uncle remain in a critical but stable condition in hospital. The father has since been released.

Detectives have said the male suspect, who is still at large, kidnapped Eliza for reasons not yet known but that it did not appear to be "random".

Long Beach Police Lieutenant Lloyd Cox told ABC news: "It appears to be very personal.

"It was not a random act that someone just picked this house to kidnap an infant from."