Prince Mohammed bin Nayef was referring to a tragedy a week ago, when a massive crane being used in work on an expansion of Mecca's Grand Mosque toppled into a courtyard, killing 108 people.
Another 402 people were injured.
Prince Mohammed, quoted by the official Saudi Press Agency, said the kingdom always "takes into consideration the safety of pilgrims as a priority".
The incident has been dealt with "in record time with the directives issued by King Salman and.... Has no more effect whatsoever on the hajj plans for this year."
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On Tuesday, King Salman sanctioned the contractor, Saudi Binladin Group, after he reviewed an investigative committee's findings that the firm was "in part responsible" for the crane collapse during severe winds.
He ordered prosecutors to prepare an indictment, excluded the company from new public projects and forbade its executives from leaving the country pending the completion of legal action.
Saudis, Iranians, Nigerians, Malaysians, Indonesians and Indians died in what was the worst hajj-related accident in years.
With more than 1.2 million pilgrims already crowding Mecca, it is difficult to see the site of the accident among the throng.