The incident took place between 10pm-10.25pm in Havant Street, near to the junction with Clock Street, Portsea on Thursday, January 12.
Three men approached a 46-year-old man and a 47-year-old man from the direction of College Street.
The group assaulted the pair before running back towards College Street.
The two men were taken to the Queen Alexandra Hospital for treatment for serious but not life-threatening head injuries.
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The first man in the group of three is described as white, 6ft 4ins tall, of medium build and with short, black hair.
The second man is described as 5ft 10ins tall, aged over 35 years, of scruffy, thin appearance, with a shaven head and stubble to the face. He was possibly wearing jeans and a jumper.
The third male is described as white, small, aged in his 20s, with short, black hair.
A spokeswoman for Hampshire Constabulary said: ‘We would like anyone with information about what took place to come forward.
‘In particular, we are keen to speak to a woman with a black and white bull terrier-type dog (pictured above) who was seen nearby at the time.
‘She might have information about what happened.’
Anyone with information should call 101, quoting 44170014862 or call Crimestoppers on 0800 555 111 where information can be left anonymously.