Hillary, 83, was guest of honor at a parade marking 50 years since he and his Sherpa guide Tenzing Norgay became the first people to reach the summit of the 29,035-foot peak.
"I have suggested to the Nepal government that they should stop giving permission and give the mountain a rest for a few years," Hillary said.
Other veteran climbers suggested limiting the number of expeditions, which turn into traffic jams on the fixed ropes and ladders that cross the icy ridges.
"Everest has become too crowded. It needs a rest now," said Junko Tabei, 64, of Japan, the first woman to reach the summit. "Only two or three teams should be allowed in a season to climb Everest."
But the Sherpas who earn their living from the backbreaking and dangerous work of guiding adventurers to the highest point on earth oppose any reduction in climbing permits.
"There are thousands of people in the region who solely depend on the trekkers and mountaineers for their income. If they don't come, these people and their families will starve," said Ang Phurba, a Sherpa guide.
Nepalese officials said they have no immediate plans to close down the mountain that brings much-needed income to this undeveloped Himalayan kingdom. Climbers are welcome as long as long as they are willing to pay, said Damodar Rana, executive vice president of the Everest Golden Jubilee Committee.
Each team of seven climbers pays a royalty of $70,000 to the Nepalese government.
A record number of people are climbing Everest this month to mark the 50th anniversary of the first successful climb.
There are an average of 12 teams on the mountain each spring. This year there have been twice that number, with more than 137 people reaching the summit in the past week alone, Nepal's tourism board said.
Reinhold Messner, an Italian who was the first to climb Everest without bottled oxygen, pleaded at a news conference on Tuesday for the government to allow only one expedition per route each season. There are about a dozen routes to the top, including the southern one that Hillary and Norgay used on May 29, 1953.
Like Hillary, Messner objected to inexperienced climbers taking on the world's highest mountain. "Why should somebody who has never been to a high peak go immediately from big cities in the West or Japan and climb Everest?" he said.
"There is no doubt that human beings were not made for such high places. We are accepted there for a few hours," Messner said, discussing the brain cell damage that occurs at high altitude, where oxygen is limited.
Not all mountaineers agree.
"Everest is a beautiful mountain. There should not be any restrictions on climbing. More and more people should be allowed up there," said Alan Hinkes, a renowned British mountaineer.
Yuichiro Miura, a 70-year-old former professional skier from Japan, achieved a record this month as the oldest Everest summit climber, and he's glad he had the chance.
"There should be strict (environmental) regulations but the mountain should not be closed," he said.
Mount Everest is littered with tents, plastic wrappings, food cans and oxygen bottles climbers have left behind on the once-pristine slopes.
"There is about 10 tons of garbage still left on Everest," said Ken Noguchi, a Japanese mountaineer who has been working for four years to clean the mountain, and just returned from Everest with 2.4 tons of refuse.
The Nepalese government requires mountaineers to bring down all their gear and trash or forfeit a $4,000 deposit.
By Laurinda Keys