In the deadliest day in K2's history, the avalanche occurred when a chunk from an ice pillar snapped away on a feature called the Bottleneck.
Wilco Van Rooijen, one of the rescued climbers
Several climbers were swept to their deaths; others froze to death after they were stranded high on the mountain.
Cpt Azeemullah Baig said a Pakistani army helicopter had already picked up the two Dutch climbers.
"Thanks to Almighty Allah, the rescue operation has started this morning," he told Reuters news agency.
Four rescue climbers reached Italian mountaineer Marco Confortola after attempts to reach him by helicopter were called off in bad weather, Pakistani guide Sultan Alam told Reuters news agency from the K2 base camp.
The rescuers were guiding Mr Confortola to the advanced base camp 6,000 metres up the slopes of K2.
The head of an Italian mountaineering group who spoke to Mr Confortola by satellite phone said his feet were in "very bad" shape from frostbite but that he could still walk and that his hands were in good condition.
Mr Confortola's brother also spoke to the stranded climber.
"Up there it was hell," Ansa news agency quoted Mr Confortola telling his brother Luigi.
"During the descent, beyond 8,000 metres (26,000 feet), due to the altitude and the exhaustion I even fell asleep in the snow and when I woke up I could not figure out where I was".
The Death Zone
The two rescued Dutchmen are being treated for frostbite in a Pakistani military hospital.
"Everything was going well to Camp Four and on [the] summit attempt everything went wrong," one of the Dutchmen, Wilco Van Rooijen, told Associated Press news agency.
He said some ropes had been laid in the wrong position - a mistake which took several valuable hours to correct, delaying the summit push until just before darkness.
As climbers descended from the peak in the dark, the ice pillar collapsed, sweeping away climbers and stranding others in the high-altitude level known as the Death Zone - where there is not enough oxygen to support life.
Pakistani authorities said three South Koreans, two Nepalis, two Pakistani porters, and French, Serbian, Norwegian and Irish climbers had died on the mountain.
Expedition organisers only learned of the avalanche after a group of climbers arrived back at the mountain's base camp on Saturday evening.
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