The last figure given by the Saudi authorities was 769.
However, a Nigerian official told the BBC that more than 1,000 bodies had been taken from the disaster site to morgues in the city of Jeddah.
Indian, Pakistani and Indonesian officials have also been quoted as saying they think more than 1,000 died.
A Nigerian Hajj official from Kano, Abba Yakubu, told the BBC’s Yusuf Ibrahim Yakasai that he had been to Jeddah, where the dead from Thursday’s crush are being processed.
Mr Yakubu said that in total, 14 lorries loaded with bodies were brought to the city.
He added that so far 1,075 bodies had been offloaded from 10 lorries and taken into the morgues. Four lorries had yet to be dealt with, he said.
Several countries have been severely critical of the way the Saudi authorities have handled the accident’s aftermath, notably Saudi Arabia’s regional rival Iran, which lost at least 228 people in the disaster.
Indian Foreign Minister Sushma Swaraj tweeted that Saudi authorities had released photos of 1,090 pilgrims who died. Pakistani and Indonesian officials have also indicated that they have been sent more than 1,000 such images.
As yet the Saudi authorities have not explained the discrepancy in the figures.
Thursday’s stampede was the deadliest incident to hit the Hajj in 25 years.
The crush occurred on Thursday morning as two large groups of pilgrims converged at right angles as they took part in the Hajj’s last major rite – stone-throwing at pillars called Jamarat, where Satan is believed to have tempted the Prophet Abraham.
As well as the fatalities, 934 people were injured.
The country’s most senior cleric, Grand Mufti Sheikh Abdul Aziz bin-Abdullah al-Sheikh, has defended the authorities, saying the stampede was “beyond human control”.
King Salman has ordered a safety review into the disaster.
The disaster is the second to strike in two weeks, after a crane collapsed at the Grand Mosque in Mecca, killing 109 people.