Several hundred policemen kept watch over the proceedings on the last day of the pilgrimage.
Monday's event passed off "without any incident", health ministry spokesman Khalid al-Mirghalani said, denying an earlier official statement that dozens of pilgrims had been taken to hospital after a "minor stampede".
The ministry said 47 people remained in hospital out of 240 injured in Sunday's crush.
Apart from the 251 people killed in the stampede, another 272 pilgrims had died of natural causes during the pilgrimage, Hajj Minister Iyad Madani said.
After repeated human tragedies over the years, King Fahd issued a royal decree overnight on Sunday to modernise the holy cities in a 20-year project.
And the council of grand ulama, the highest religious body in Saudi Arabia, said it would meet on Thursday in Makka to seek a solution to halt the stampedes.
Grand Mufti Shaikh Abd al-Aziz explained Sunday's stampede as "the will of God", but stressed the council intended "to seek by all means to avoid similar accidents" in the future.
The Jamarat, the name given to the place where pilgrims symbolically stone three pillars representing the devil, has been a regular troublespot during the several day pilgrimage.
Over three days, hundreds of thousands of pilgrims converge on the narrow site set in the valley of Mina, several miles east of Makka. The construction of a flyover to reduce congestion has failed to halt the tragedies.
Dying in Makka
The deaths have not shocked many people, with several pilgrims certain that those who die during Hajj enter paradise.
Dying while on Hajj is considered
to be very auspicious
"I wish I was among the pilgrims who died on Sunday," Kamal Shahada, an Egyptian pilgrim, said.
"I would have gone to heaven, because dying in these holy sites of Islam would assure one a place in heaven," he said, echoing a widespread conviction in the Islamic world.
Libyan Muhammad Taylamun agreed. "The two million faithful who gathered every year at the holy sites for the pilgrimage hope to have the honour of being buried in this sacred soil," he said.
The scale of the tragedy which cast a shadow over the Hajj
certainly provoked compassion among the gathering, but fatalism predominates among "the guests of God".
"Those who died will be missed by their families and friends but they have a chance no one else can have by dying on the holy land of Islam where they are then buried," said a Bangladeshi.
"When our ancestors left for the pilgrimage to Makka they bid farewell to their friends and set off by camel or boat for a journey which often lasted several months each way," said Abd Allah Muhammad, a Senegalese.
King Fahd has ordered the holy
cities to be modernised
"The death of a pilgrim, which would be known only when the caravan returned, was met with respect and piety because of the honour accorded to he who ended his days in Makka and the holy sites in Saudi Arabia," he said.
Last year 14 pilgrims were killed in a stampede during the first day of the stoning ritual and 35 in 2001, while the 1998 Haj saw 118 killed and more than 180 hurt at the pillars.
The worst Hajj disaster struck in July 1990, when 1426 pilgrims were trampled or asphyxiated to death in a tunnel in Mina.
Numerous other deaths have been caused by fires in the pilgrims' camps.