Police are still keen for climbers and pilots in the area to keep a look out for anything of interest. "The search team are obviously disappointed with the result and our thoughts are with the families in Australia and Germany," Mr Swanson added.
It is not yet known if any family members are intending to travel to New Zealand.
The families have also been warned that the bodies may never be found.
About 60 bodies of dead climbers have never been recovered from Aoraki-Mt Cook National Park.
The death toll for the national park now stands at 238.
On Christmas Day, Dr Bishop, a father of two, decided to attempt the summit that had eluded him twice before.
It is understood he met the German pair at the Plateau Hut.
After hearing that the climbers had been reported missing, the Bishop family said they hoped that they had been sheltering from bad weather.
Dr Bishop's elder son, Joshua, said on Thursday: "Everyone is still having faith and hoping for a good outcome ... but we're just coming to terms with the fact there's been a tragedy and probably all three of them have lost their lives."
Dr Bishop, who started climbing as a medical student about 30 years ago, had not planned to climb with the Viellehners but after they met, they decided to attempt the summit together.
Joshua Bishop, 27, said his father "wasn't a Mt Everest, alpha climber" but a highly experienced climber who loved the thrill of reaching a summit.
"He loved being up there and close to his God."
