The plane's emergency locator beacon was activated on Wednesday night when the plane was en route from the South Pole to the Italian base at Terra Nova Bay.
The search in mountainous terrain about 450 kilometres north of the South Pole was initially suspended overnight due to strong winds and heavy snow.
The search resumed again this morning but has once again been suspended because of high wind and heavy cloud cover.
RCCNZ spokesman Mike Roberts says rescuers will try to reach the plane as soon as conditions permit.
He says the rugged terrain means sending in a helicopter is the preferred option, but mountain rescue experts and medics are also prepared to make a land-based approach if feasible.
"We have two helicopters on standby at the moment... and they will fly in as soon as conditions allow," he told Radio New Zealand.
The missing Twin Otter was operated by Canadian company Kenn Borek Air, and its pilot was highly experienced in polar flight.
The rescue centre says the plane was carrying emergency equipment and supplies for five days.
New Zealand is coordinating the rescue with US authorities at McMurdo Station.
Pilot Bob Heath was reportedly among the three men on board. His friend and occasional co-pilot Tony Szekely remains optimistic.
"Bob possesses the skills to make the most of what's available," he said.
"He can maximise the performance of the aircraft. He's one of the best pilots I know."