The Americans - Kurt Blair, 56, and Carlos Romero, 50, - are certified alpine guides, according to the website of the American Mountain Guides Association.
New Zealand police did not name the Canadian climber, citing the need to notify his family.
The men flew to a hut part way up the mountain on Saturday to begin their ascent and were reported missing on Monday when they did not arrive to meet their prearranged transport after the climb.
Searchers hours later found several climbing-related items believed to belong to the men, but no sign of them, police said.
Search efforts did not resume Tuesday due to deteriorating weather conditions on Aoraki, also known as Mount Cook, with heavy rain and snow forecast.
Operations were unlikely to begin again until conditions improved, expected to be on Thursday.
Aoraki is 3724 metres high and is part of the Southern Alps, the scenic and icy mountain range that runs the length of New Zealand's South Island.
The peak is popular among experienced climbers.
Its terrain is technically difficult due to crevasses, avalanche risk, changeable weather and glacier movement.
More than 240 deaths have been recorded on the mountain and in the surrounding national park since the start of the 20th century.
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