The Hajj Supreme Committee said 202 pilgrims have died since arriving in the kingdom, mainly the elderly or infirm.
In Mecca on Monday, a fire in a hotel left a number of pilgrims suffering from smoke inhalation.
The SPA quoted General Mansur al-Turki, an interior ministry spokesman, as saying that "13 pilgrims suffering from smoke inhalation were admitted to hospital, where their condition is stable".
The SPA also said that on Tuesday, prince Nayef bin Abdul Aziz, who heads the Hajj Supreme Committee, will inspect security arrangements at Mecca.
Earlier this month Saudi Arabia agreed to admit more than a thousand Iraqi pilgrims stranded at the border where they were denied because they did not have the correct visas for hajj.
At dawn on Friday the pilgrims will make their way to Mount Arafat where they will typically spend the day in prayer.
Later pilgrims return to Mina to celebrate Eid al-Adha, the Feast of the Sacrifice, on Saturday.
Pilgrimage to Mecca is one of the five pillars of Islam and undertaking it is considered an obligation for Muslims at least once during their lives, if they can afford to do so.