Police have recovered debris which is believed to be from the missing boat incident on Lake Hauroko in Southland yesterday.

A police spokeswoman informed there was no planned search activity today.

"The SAR team is assessing what next steps they will be taking."

Invercargill police were notified late on Friday that a boat and its two occupants were missing on the lake.

After a search was undertaken using a local boat operator on Saturday, police found a body near Teal Bay, at the southern end of the lake.

Police continued to search Lake Hauroko on Sunday a helicopter and jet-boat for the one remaining missing occupant and the boat.

Southland District councillor George Harpur, who represents the area, said the death and disappearance were "an unfortunate shock".

Harpur had long hunted and travelled in the lake area, but weather and lake conditions could change within minutes.

He had also seen large waterspouts form on the lake in high winds.

Paul Roff, owner-operator of Wairaurahiri Wilderness Jet, said the southern Teal Bay area was generally "pretty safe", but conditions could change quickly.

A New Zealand Tramper internet site discusses the Teal Bay hut and says "boating on this lake can be harrowing as weather funnels out of the mountains, so pick your day!"

Queenstown Lakes District harbourmaster Marty Black said the lake was out of his patch, but he was familiar with it, and westerly winds could generate difficult, choppy conditions.

Lake Hauroko is a 30km-long, S-shaped lake in Fiordland National Park.

It covers 63sqkm and, at 462m deep, is New Zealand's deepest lake.