The pair reached the summit of Mount Everest at 11.30am on 29 May 1953, cementing a long-lasting friendship between the two climbers that blossomed into ongoing ties between the two countries.
Nepal begun commemorating the date as International Everest Day after Hillary's death in 2008, but New Zealand has not followed suit.
The day has been celebrated in Nepal and by the Nepali diaspora ever since, as an occasion to promote alpine tourism and mark the special bond that exists between Nepal and New Zealand.
"The seed of this wonderful relationship between our two countries were sowed when those two great mountaineers sat foot on Sagarmatha together," said Dinesh Khadka, honorary consul of Nepal in Auckland, while speaking at Auckland's Everest Day celebrations.
Sagarmatha is Mount Everest's local name.
"Since that day, the bond has grown even stronger," Khadka said.
"Considering this, I have been fighting with the New Zealand government for our two demands. First is the simple question: Two people climbed Everest, why only one was honoured with the title of 'sir'? And second is our long-standing demand of giving Everest Day an official status in the government's official calendar."
The Auckland event was organised by the Non-Resident Nepali Association New Zealand, the Himalayan Trust, the Embassy of Nepal in Canberra and the consul in Auckland.
"We will be running a signature campaign closer to this year's general elections with a call to make this day an official celebration," Khadka said.
Other celebrations took place in Hamilton over the weekend, organised by the Nepal New Zealand Waikato Friendship Society and Sagarmatha Wellbeing and Harmony Trust of New Zealand.
This year's celebrations will end with an event at parliament organised by the Nepalese Society of Wellington on Wednesday.
In Auckland, apart from the usual dose of Nepali cuisine, attendees were treated to traditional sherpa welcome songs and dances. One of the highlights of the event was the unveiling of a 3D model of Mount Everest that traces Hillary and Tenzing's 1953 route.
As has been the tradition, the organisers auctioned a $5 note signed by Hillary for the Himalayan Trust's ongoing work in Nepal. Last year, the bill went for $1300. This year, the highest bidder picked up the coveted note for $2100.
The organisers thanked the trust for its ongoing work to build schools, hospitals and health clinics across the Solukhumbu region in the foothills of Mount Everest.