Daniele Nardi and Tom Ballard were attempting the 8,126-metre climb in Pakistan’s Himalayas, one of the hardest mountaineering feats in the world, when they went missing.
They were last heard from on February 24, when Nardi called his wife from camp four at around 6,000 metres up the world’s ninth-highest mountain.
Ballard’s girlfriend told the Sunday Times that she had lost hope in finding the pair.
“It’s pointless. No hope any more. It is hopeless,” Stefania Pederiva, an Italian woman who lives in the Dolomites, told the paper.
Ballard is the son of famed British climber Alison Hargreaves, who became the first woman to climb Mount Everest unaided in 1995 but died that year while descending from a summit of Pakistan’s K2, the world’s second-tallest mountain.
The missing pair were attempting to climb Killer Mountain by a route that had never been successfully used to reach the peak.
Two Pakistani climbers who were part of the mission had earlier abandoned the climb, according to the Italian embassy in Pakistan.
Rescue teams were initially forced to wait for permission to send up a helicopter after Pakistan closed its airspace on Wednesday in response to heightened tensions with India.