Police are still searching for the person who attacked an elderly man at a park in Remuera in Auckland on Wednesday afternoon.

A 72-year-old man was playing with his grandchildren at Little Rangitoto reserve on Upland Road when a young man came up to him and attempted to start a conversation.

He then struck the elderly man in the neck with a knife.

The man did not require medical attention, but was shaken by the incident.

Although the man's injuries were minor, Detective Senior Sergeant Paul Newman described the incident in the affluent Auckland garden suburb as "serious and concerning".

Newman could not comment on what the men talked about but said there had been no argument or provocation.

The offender was last seen heading on foot in the direction of Benson Road.

He's described as Caucasian, of medium build and olive-skinned. He's thought to be aged in his late teens or early 20s.

There were about twenty people in the park, which has views towards the Hauraki Gulf.

Anyone with information should call police immediately.