The hajj, a pillar of the Muslim religion which last year drew about two million faithful, will take place despite Friday's tragedy, Saudi authorities said as crowds returned to pray a day after the incident.
Hundreds of thousands of pilgrims had already arrived in Mecca when the massive red and white crane toppled over during a Friday thunderstorm.
"We will investigate all the reasons and afterwards declare the results to the citizens," Salman said after visiting the site, one of Islam's holiest, yesterday.
But there was little mourning among pilgrims, who snapped pictures of the collapsed metal and continued with their prayers and rituals.
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"I wish I had died in the accident, as it happened at a holy hour and in a holy place," Egyptian pilgrim Mohammed Ibrahim told AFP.
Om Salma, a Moroccan pilgrim, said "our phones have not stopped ringing since yesterday with relatives calling to check on us".
Indonesians and Indians were among those killed when the crane collapsed, while the injured included Malaysians, Egyptians, Iranians, Turks, Afghans and Pakistanis.
A Saudi official said the hajj, expected to start on September 21, would go ahead despite the tragedy.
"It definitely will not affect the hajj this season, and the affected part will probably be fixed in a few days," said the official, who declined to be named.
The pilgrimage is a must for all able-bodied Muslims who can afford it.
An investigative committee has "immediately and urgently" begun searching for the cause of the collapse, SPA reported.
The cranes soar skywards over the sprawling expansion taking place beneath the Mecca Royal Clock Tower, the world's third tallest building.
For years, work has been under way on a 400,000- square-metre enlargement of the Grand Mosque to allow it to accommodate up to 2.2 million people at once.