There have been other close calls. In 2013, Chanon Thompson, a Texas woman searching for the treasure in New Mexico, got lost near Bandelier National Monument and spent a frigid night in the wilderness. She was rescued the next day.

Mr. Fenn has said that the treasure is somewhere in the Rocky Mountains and 5,000 feet above sea level, a suggestion that has tempted people into some of the more unsparing wilderness in the southwest. He recently specified that it is not in an area that an 80-year-old would find difficult to gain access to.

Mr. Bilyeu’s ex-wife, Linda Bilyeu, who first reported his disappearance, has since said that Mr. Fenn’s treasure was a scam and a hoax. On Tuesday, she too called for Mr. Fenn to end the search. “He’s endangering lives for his own selfish reasons,” she said.

Mr. Fenn said he planned to change the hunt in some way, but had no details yet.

“I am thinking of ways to make the search for my treasure safer, and expect to make an announcement in the next few days,” he said.

Mr. Fenn, 86, is a cheerful eccentric whose Santa Fe gallery attracted frequent visits from an eclectic group of celebrities in the 1970s and 1980s. A 1986 profile in People magazine reported that President Gerald Ford, the former first lady Jacqueline Kennedy, and entertainers like Robert Redford, Cher and Steve Martin were among the customers paying high prices for oil paintings and Native American art and artifacts.

He dreamed up the treasure hunt several years after that profile was published, when he learned he had kidney cancer. Originally, he had planned to have himself interred with the buried riches, but after recovering from the disease, he decided to create the treasure hunt. And so, he said, shortly before publishing “The Thrill of the Chase,” he went out alone and buried the treasure. In a New York Times profile last year, he estimated that it was worth $2 million.