Other teams on K2, which is on the Pakistan-China border, had turned back because of dangerous snow conditions.
The deaths, if confirmed, would mean more than 20 mountaineers killed in a month, making it one of Pakistan's deadliest climbing seasons for years.
They include 10 foreigners and a local porter shot dead by militants at Nanga Parbat in June.
British climber and explorer Adrian Hayes was in one of six other teams that abandoned attempts on K2 over the weekend.'Forceful character'
Mr Hayes told the BBC the climbers took the decision to retreat from Camp 2 after sherpas reported bad weather up ahead.
"The sherpas on our team went up to Camp 3, and they found themselves wading through four feet of snow. An avalanche came very near them, within 20m. They came down a little bit spooked and said it's impossible, we can't go up right now," he said.
But while most teams decided to turn back, including a Swiss team and a Spanish climber, the New Zealanders decided to head for Camp 3.
"I think that they took the view that the retreat from Camp 2 was a little bit premature. The conditions were bad and I think they acknowledged that. But they wanted to go up to Camp 3 to check it out themselves," said Mr Hayes.
He described Marty Schmidt as a "forceful character", saying he was "highly assertive, very strong, very competent, as was his son (Denali)".
"Marty was extremely proud of Denali, and Denali looked up to his father greatly. They climbed together... and they died sleeping together, which is such a tragedy.
He described K2 as a "dangerous mountain, very difficult, very steep".
"Obviously there's a lot of shock here at the base camp because they were so experienced. But having said that, mountaineering is a risky sport (and) death is an expected part and parcel of it," he said.
Other climbing accidents this summer have seen three Iranians and a German die on Broad Peak, a Polish climber die on G2, and three Spaniards killed on G1, he said.