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Emergency services responded to the incident at Maruia Falls in Shenandoah, near Murchison, on Friday.
One person was pulled from the water. However, a second person is still outstanding. He is a male in his twenties from Christchurch.
A police spokesperson said Inclement weather has paused the active search but they continue to consider all viable possibilities in regards to the missing male.
They said they hope to resume the search later this week.
"We remain in contact with the man's family and will continue to do so to provide them with any necessary support.
"We'd like to thank all the people who have assisted in and who will continue to assist in the search. We wouldn't be able to operate in the challenging environment without their efforts."
Police remain in contact with the National Dive Squad, Swift Water Rescue Teams and other local SAR and river experts to assess the searching conditions.