Hosting the pilgrimage is a matter of prestige for Saudi rulers, for whom the custodianship of Islam's holiest sites is their most powerful source of political legitimacy.
But barring overseas pilgrims has caused deep disappointment among Muslims worldwide, who typically save for years to take part.
"If we can guarantee that there will be full control (of Covid) and ensure the safety of pilgrims too, which is a priority for the kingdom and its leaders, the hajj can happen again in the future as it was before," the health minister said.
After the stoning ritual, pilgrims return to the Grand Mosque in Mecca to perform a final "tawaf" or circling of the Kaaba.
The Kaaba is a cubic structure that is the focal point of Islam and draped in a gold-embroidered black cloth.
State media said that an army of 3,500 workers was tasked with sterilising the Grand Mosque ten times a day to prevent any spread of infection.
This year's hajj is being held at a time when new variants of the virus are causing global concern.
Saudi Arabia has recorded more than 510,000 cases of coronavirus including 8,089 deaths.
The participants were chosen in a lottery among 558,000 Saudi residents and nationals, who had to be between 18 and 65 years old, vaccinated and free of chronic diseases.
All the workers mobilised for the hajj have been fully vaccinated as well, authorities say.
Saudi Arabia's King Salman said Monday in a televised speech that "the kingdom's efforts to limit the effects of the coronavirus have been successful."
The strict preventive measures "have enabled pilgrims to perform the hajj," he added.
