A man has come within millimetres of death after a savage fight between his Labrador and another dog in Melbourne's Bayside.

Cam McIntyre was running on the beach in Brighton about 11.30am on Saturday when the large dog attacked his pet, wrapping its jaws around its head.

Desperate to save his beloved dog, Mick, Mr McIntyre tried to separate the animals, suffering a deep wound to the hand.

"I didn't think so much of it. There was a bit of a frenzy going on," he told radio station 3AW.