Al-Turki said the final number of pilgrims would not be known until the Hajj climaxes on Friday, when the faithful start moving towards Mount Arafat where they will spend the day praying and asking for God's forgiveness at the summit, symbolic of waiting for the last judgment.
Thousands of Saudi security forces have been deployed along the routes to be used by the pilgrims.
Official media said security and health authorities have been mobilised to ensure the safety of the faithful during often risky rituals.
For pilgrims streaming in from all continents, the Hajj is a crowning moment of faith, a duty for all able-bodied Muslims to carry out at least once if they can afford to. It is one of the five pillars of Islam.