Six people were also injured when the aircraft, carrying construction workers to build a military outpost, smashed into a cliff as it tried to land at the remote site near the Malaysian border.
The start of the mission to retrieve the bodies was delayed for several hours today by bad weather but clouds cleared later, allowing a helicopter to fly to the remote area.
It was carrying mountaineering equipment so that rescuers - mainly military and search and rescue agency personnel - could reach the wreckage on a cliffside in Malinau district in North Kalimantan province.
"It's bright and sunny now and rescuers said they did not face much of a problem. We believe we will be able to evacuate all the bodies today and airlift them" to Tarakan, a town in northern Borneo, he added.
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Three other aircraft were on standby to help if needed.
President Susilo Bambang Yudhoyono expressed his "deep sorrow" at the deaths.
"Hopefully the families of the soldiers and other victims will find fortitude in the face of this tragedy," he said in a tweet.
Once the bodies have been evacuated, an investigation into the cause of the crash will begin.
Military officials said they suspect it was caused both by bad weather and a problem with the back rotor blades, which appeared to spin out of control just before the helicopter hit the cliff.
Eight of those killed were civilian construction workers and five were crew members, who were military personnel. The six survivors were still in hospital receiving treatment for burns.
There have been numerous fatal air crashes over the years in Indonesia and some have involved military aircraft.