Switzerland's Ueli Steck and Simone Moro from Italy were at 7,470m (24,500ft) when the brawl occurred.
The pair allegedly ignored orders to hold their climb and triggered an icefall which hit the Sherpas laying fixed ropes. The climbers deny this.
Both sides have since reached a peace deal, reports say.
Mr Steck told the BBC that their three-man team - which included Briton Jonathan Griffith - was nearing Camp Three on Saturday, when the "conflict" broke out.
He said they had been keeping a respectful distance so as not to disturb the work of the Sherpas laying ropes.
The climbers continued to Camp Three but later descended to Camp Two to "finish the discussion" and were met by more than 100 angry Sherpas, who began to beat them and throw rocks, Mr Steck said.
He said the Sherpas threatened to kill the climbers if they did not leave the camp.
One of the Sherpas threw a pocket knife at Mr Moro but "luckily [it] just hit the belt of his backpack", Mr Steck said, adding that they escaped with no serious injuries.
Mr Steck said the conflict was the symptom of a long-term problem of "cultures", but did not elaborate.
Ang Tshering Sherpa, the former president of the Nepal Mountaineers Association, told the BBC that climbing leaders of various teams at base camp helped broker a peace deal on Sunday.
Exact details are not very clear, but the two sides clearly had a misunderstanding, Mr Ang said.
In a statement, Mr Moro said that "getting hit by chunks of ice is a very natural occurrence" on an ice face. "As it stands, no Sherpa has come forward to show any injury."
"The climbers believe that the lead Sherpa felt that his pride had been damaged as the climbers were moving unroped and much faster," the statement added.
When they returned to their tents, Mr Moro said a mob of guides had grouped together to attack them.
"[The guides] became instantly aggressive and not only punched and kicked the climbers, but threw many rocks as well," said Mr Moro.
More than 3,000 people have scaled Mount Everest since it was first conquered by Edmund Hillary and Tenzing Norgay in 1953.
Straddling Nepal and China, the world's highest mountain has an altitude of 8,848m (29,029ft).
Police in Nepal are investigating an alleged fight between two famous European climbers and their Nepalese mountain guides on Mount Everest.