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Hans Christian Tornmarck (27) went hunting by himself on May 12 and was due out three days ago.
Sergeant Mathew Tailby, of the West Coast Police Search and Rescue, said five teams have been in the Karangarua Valley on Saturday focusing on the upper reaches of Regina Creek in vastly improved weather conditions.
Sgt Tailby said teams on Saturday found a campsite believed to be Mr Tornmarck's, including a sleeping bag and tent.
A helicopter assisted with an aerial search.
Sgt Tailby said the search was expected to wind down on Saturday evening due to the tricky terrain and it would resume on Sunday.
An alpine team, a Land SAR dog and additional Land SAR volunteers from Westport joined the search on Saturday.
Mr Tornmarck's family in Sweden have been notified of the search and are being kept informed of any developments.
Police would still like to hear from anyone who has been in the Karangarua area, south of Fox Glacier, in the past week.
Anyone with any information or sightings is asked to contact Greymouth police on (03) 768-1600.
Search teams have located a campsite believed to be that of the missing man, including a sleeping bag and tent.
The search is expected to wind down this evening due to the tricky terrain and the need to rotate searchers.
It is intended to resume tomorrow.