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Saudi Arabia has deployed 100,000 security personnel to oversee the Haj pilgrimage.
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308 of these Haj pilgrims have died.
SPA said Salman made the same appeal in phone calls to British Prime Minister David Cameron, Russian President Vladimir Putin and French President Francois Hollande.
Saudi Arabia was in a similar position in 1998, until a rebound in oil prices alleviated the need for drastic measures.
Firefighters "rescued two pilgrims who were hurt" by the fire in an eighth-floor room of the unnamed hotel, the agency said.
The Saudi king sanctions Binladin Group after deadly crane collapse. An investigative commission had concluded that the company "was in part responsible" for Friday's tragedy.
Saudi soldiers died "in the line of duty while protecting the nation's borders".
The incident also left 331 others injured.
The Haj pilgrimage, which starts next week, will proceed unaffected by the incident, Saudi officials confirmed.