Mr. Worsley meets with Britain's Prince William at Kensington Palace in 2015. (John Stillwell/AFP/Getty Images)

Henry Worsley, a British explorer attempting the first unassisted solo crossing of Antarctica, died Jan. 24, 71 days after setting out and within 30 miles of his goal. He was 55.

His death was announced on his online expedition diary and by the Endeavor Fund, a British organization established to assist the recovery of wounded veterans. Mr. Worsley had set out on his trek in a fundraising effort on behalf of that group.

Mr. Worsley had been suffering from increasing exhaustion and dehydration during the voyage, posting updates by satellite phone that began with optimism and ended in desperation.

“This is just the best place on Earth right now,” he said on the first day of the trip, in November.

His final message on Jan. 22 was both a call for help and a cry of frustration. “It is with sadness that I report it is journey’s end — so close to my goal,” he said.

Mr. Worsley was soon airlifted off the ice — after covering more than 900 miles — and died at a medical facility in Punta Arenas, Chile, said his wife, Joanna, in a statement. He was reported to be within 30 miles of completing the trek.

Her statement described the cause of death as “complete organ failure.” He had undergone surgery for bacterial peritonitis, an infection in the abdomen that can lead to septic shock.

Mr. Worsley, a former British military officer who had served in Bosnia, Kosovo and Afghanistan, pulled his own sled with food and supplies in an attempt to complete the projected route of adventurer Sir Ernest Shackleton a century ago.

Shackleton’s ship became trapped in the ice off Antarctica in January 1915, leading to an epic rescue that included Shackleton and five others sailing a small boat 800 miles to reach help on South Georgia Island.

Mr. Worsley had expected his journey to take between 75 and 80 days — which would have been the first without assistance from sled dogs or other support such as airdrops.

On Jan. 22, with his voice still strong but tinged with sorrow, he posted an audio message saying he could no longer continue.

“My journey is at an end,” he said. “I have run out of time . . . [and] the sheer ability to slide one ski in front of the other to travel the distance required to reach my goal.”

Mr. Worsley had noted his fascination with early polar explorers, including Norwegian explorer Roald Amundsen, who in 1911 became the first person to reach the South Pole. But Shackleton had a special significance for Mr. Worsley, who came across a photo of the failed expedition as a boy.

“That fired my imagination,” he told the podcast “Inspiring Adventurer.”

In the winter of 1915, Shackleton’s ship, the Endurance, became trapped in an ice floe in the Weddell Sea. For more than nine months, the 28-person crew stayed aboard the immobilized boat, which later was crushed by the ice and sank.

As their rations dwindled, Shackleton brought his men to nearby Elephant Island, then embarked on a trip across open ocean in a tiny lifeboat to seek help.

Twenty months after their ship was first caught in the ice, the entire crew of the Endurance landed in Punta Arenas, battered but miraculously alive.

“Shackleton and his style of leadership became an important part of my character,” Mr. Worsley told Inspiring Adventurer.

Besides his wife, survivors include two children, Max and Alicia.

Britain’s Prince William, who helped back Mr. Worsley’s expedition, said he and his brother, Prince Harry, “were incredibly proud to be associated with him.”