Its report proposes that applicants must already have climbed a Nepali peak of at least 6,500m (21,325ft).
They should also have to provide a certificate of physical fitness, and employ experienced guides, it adds.
Earlier this year at least 11 people died or went missing on Mount Everest.
Nine of the deaths occurred on the Nepali side of Everest and two on the Tibetan side, with four of them blamed on overcrowding.
The panel's report also proposes a fee of at least $35,000 (£29,000) for those wanting to climb Everest, and $20,000 for other mountains higher than 8,000m.
"We will take this forward by amending the laws and regulations. We will make our mountains safe, managed and dignified," Tourism Minister Yogesh Bhattari told reporters.
Nepal is home to eight of the world's 14 highest mountains, and foreign climbers are a major source of revenue.
The Nepali panel was staffed by government officials, climbing experts and climbing community agencies.
It was set up after criticism from experienced climbers and guides of the system that allows anyone who pays $11,000 to climb Everest.
Nepal's government issued a record 381 permits this season.