At least 11 people have died and three remain missing after groups of pilgrims hiking to a religious celebration in Papua New Guinea got lost in the mountains.

At least 21 people were rescued by helicopter on Sunday and Monday from the Sarawaget range in Morobe province. They had been attempting to reach Indagen for a celebration of the 100th anniversary of the arrival of Lutheran missionaries.

However according to helicopter pilot Jurgen Ruh, walkers coming from both Pindiu in the south-east and the city of Lae in the south-west became lost or succumbed to the difficult conditions and terrain.

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On Tuesday the National reported 16 had died. “Walking in from Lae you have to go over 11,000 feet [3,300 metres] which is almost twice as high as Australia’s highest mountain,” Ruh told Guardian Australia.

“Morning temperatures are about six or eight degrees, and the conditions, with some rain, will be colder. Then with wind it really gets down to your bones and you won’t last long.”

He said many people who had made the journey were city dwellers and were not prepared with appropriate clothing or food. “The air is thin and everything that could go against you, went against them.”

Ruh said his helicopter could only take three people at a time. Nine were rescued on Sunday and another 12 on Monday. Eight people went on foot to search for bodies and to clear a landing area for the helicopter, but he said that after four flyovers he could not find them.

“I’ve got a strong suspicion they walked out again, that they didn’t stay as long as they thought they would [overnight],” he said.

“Either way we have not found the people … I’ve now requested for the defence force to take over. It’s beyond my capability now to do anything else.”

The PNG prime minister, James Marape, and the governor general, Sir Bob Dadae, both attended the event. On Monday they and the Kabwum MP Patrick Bassa led mourning for the dead and missing walkers.

Bassa said the deaths highlighted the difficulties of travel in PNG and appealed to Marape to fund a road from Lae to Kabwum, the National reported.