The bodies of three Italian climbers have been found on Mont Blanc in the French Alps, three days after they set out to climb Europe’s highest peak, rescue workers have said.

The body of Luca Lombardini was recovered by the mountain police rescue service. The bodies of his brother and his fiancee were located nearby but have yet to be recovered.

“They are probably buried under rocks and ice in an area covering a few dozen square metres,” a rescue service official said.

They were found at about 1pm local time at the foot of the Aiguille Verte (Green Needle), a peak in the Mont Blanc massif.

“They were going along a ridge at an altitude of 3,400 to 3,500 metres [11,100-11,500ft], and it seems they slipped and fell together,” the official said.

The ascent was a birthday present for Luca, who was joined by his fiancee and his brother Alessandro, who was a mountain rescue worker in Bardonecchia, near the French border, Italy’s Ansa news agency reported.

The first body was recovered after rescuers cut the cord linking the climbers. Attempts to recover the other two will resume on Saturday morning.

The accident brings to 15 the death toll on Mont Blanc so far this climbing season. Fourteen people died and two went missing last year.

Around 300 climbers a day attempt to reach the top, and overcrowding has increased the risks. Officials in July began to limit access on the most popular route by turning away climbers who did not have reservations at the 120-bed Goûter refuge.

The heatwave that has gripped much of Europe in recent weeks has made conditions more treacherous, causing more ice to melt and making the ground more unstable.