At least 323 of those who died were Egyptians, most of them succumbing to heat-related illnesses, two Arab diplomats coordinating their countries' responses told AFP.
"All of them (the Egyptians) died because of heat" except for one who sustained fatal injuries during a minor crowd crush, one of the diplomats said, adding the total figure came from the hospital morgue in the Al-Muaisem neighbourhood of Mecca.
At least 60 Jordanians also died, the diplomats said, up from an official tally of 41 given earlier on Tuesday by Amman.
The new deaths bring the total reported so far by multiple countries to 577, according to an AFP tally.
The diplomats said the total at the morgue in Al-Muaisem, one of the biggest in Mecca, was 550.
The hajj is one of the five pillars of Islam and all Muslims with the means must complete it at least once.
The pilgrimage is increasingly affected by climate change, according to a Saudi study published last month that said temperatures in the area where rituals are performed were rising 0.4 degrees Celsius (0.72 degrees Fahrenheit) each decade.
Temperatures hit 51.8 degrees Celsius (125 Fahrenheit) at the Grand Mosque in Mecca on Monday, the Saudi national meteorology centre said.
Heat stress
Earlier on Tuesday, Egypt's foreign ministry said Cairo was collaborating with Saudi authorities on search operations for Egyptians who had gone missing during the hajj.
While a ministry statement said "a certain number of deaths" had occurred, it did not specify whether Egyptians were among them.
Saudi authorities have reported treating more than 2,000 pilgrims suffering from heat stress but have not updated that figure since Sunday and have not provided information on fatalities.
At least 240 pilgrims were reported dead by various countries last year, most of them Indonesians.
AFP journalists in Mina, outside Mecca, on Monday saw pilgrims pouring bottles of water over their heads as volunteers handed out cold drinks and fast-melting chocolate ice cream to help them keep cool.
Saudi officials had advised pilgrims to use umbrellas, drink plenty of water and avoid exposure to the sun during the hottest hours of the day.
But many of the hajj rituals, including the prayers on Mount Arafat which took place on Saturday, involve being outdoors for hours in the daytime.
Some pilgrims described seeing motionless bodies on the roadside and ambulance services that appeared overwhelmed at times.
Around 1.8 million pilgrims took part in the hajj this year, 1.6 million of them from abroad, according to Saudi authorities.
Unregistered pilgrims
Each year tens of thousands of pilgrims attempt to perform the hajj through irregular channels as they cannot afford the often costly procedures for official hajj visas.
This places these off-the-books pilgrims at risk as they cannot access air-conditioned facilities provided by Saudi authorities along the hajj route.
One of the diplomats who spoke to AFP on Tuesday said that the Egyptian death toll was "absolutely" boosted by a large number of unregistered Egyptian pilgrims.
"Irregular pilgrims caused great chaos in the Egyptian pilgrims' camps, causing the collapse of services," said an Egyptian official supervising the country's hajj mission.
"The pilgrims went without food, water, or air conditioning for a long time."
They died "from the heat because most people had no place" to take shelter.
Earlier this month, Saudi officials said they had cleared hundreds of thousands of unregistered pilgrims from Mecca ahead of the hajj.
Other countries to report deaths during the hajj this year include Indonesia, Iran and Senegal.
Most countries have not specified how many deaths were heat-related.
Saudi Health Minister Fahd bin Abdul Rahman Al-Jalajel said on Tuesday that health plans for the hajj had "been successfully carried out", preventing major outbreaks of disease and other public health threats, the official Saudi Press Agency reported.
Health officials "provided virtual consultations to over 5,800 pilgrims, primarily for heat-related illnesses, enabling prompt intervention and mitigating the potential for a surge in cases," SPA said.
