"So far, the number of confirmed death is 345 and the number of injured in hospital is 289," Hamad bin Abdullah al-Manei told reporters.
Al-Maneh said the stampede was caused by "unruly pilgrims, and a problem of luggage".
"Today, just after sunset, there was a big rush among the pilgrims which led a group of them to be killed or wounded."
A medical source at Mina General Hospital told AFP that the number of injured had reached 600.
After the crush at the northern entrance of Mina's Jamarat Bridge, a witness, who gave his name only as Saeed, described the scene to Al Jazeera television.
"It was very difficult to reach the first Jamarat-throwing and I saw bodies lined up on the ground," he said. "One pilgrim has lost his family among the crowd."
Police made a circle around the place trying to get people out, he said.
One Egyptian pilgrim on the scene told AFP: "I saw pilgrims falling under the feet of other pilgrims. I don't know how many people died, but I know that it is in the dozens."
"I saw pilgrims falling under the feet of other pilgrims"
The stoning of Satan is the riskiest episode of the Hajj as pilgrims jostle to throw their stones at the pillar.
A total of 251 people were trampled to death in the 2004 Hajj as people panicked during the ritual stoning.
The stoning ritual, which is spread out over three days, marks the final part of the Hajj pilgrimage for the more than two million Muslims who have flocked to Makka from around the world.
Pilgrims were trampled to death
at the crowded ritual
In 2003, 14 pilgrims, including six women, were killed in a stampede during the first day of the stoning ritual, and 35 died in 2001, while in 1998 the Hajj saw 118 killed and more than 180 hurt at Mina.
The deadliest toll of the pilgrimage was in July 1990 when 1426 pilgrims were trampled or asphyxiated to death in a stampede in a tunnel, also in Mina.
Following the courise of a journey made by Prophet Mohammed over 1400 years ago, pilgrims flocked to the plain of Arafat, south of Mina, on Monday to pray for mercy in the central rite of the Hajj.
Before coming to Mina on Tuesday, many spent the night in the sacred site of Muzdalifah where they collected pebbles for the stoning ritual.
Thousands of security
officers are monitoring the Hajj
The Hajj is one of the five pillars of Islam and a duty for all Muslims to undertake it at least once, if their means and health permit.
The latest incident comes days after 76 people were killed when a hostel in the heart of Makka collapsed last week.
Almost 60,000 security, health, emergency and other personnel were involved in organising this year's Hajj, trying to prevent the deadly incidents that have marred it in recent years from being repeated.