The number of Indonesians killed in a stampede at the hajj rose to 41 Monday with scores more still missing, an official said, warning Jakarta faces a "race against time" to identify its citizens who died.

The stampede on Thursday during a ritual stoning of the devil near the holy Saudi city of Makkah killed 769 people, the worst disaster to strike the annual Muslim pilgrimage in a quarter of a century.

At least 144 Iranians died in the crush -- the highest confirmed toll among foreign nationalities -- sparking a war of words between regional rivals Saudi Arabia and Iran.

Indonesia, the world's most populous Muslim-majority country, initially indicated only a handful of its citizens died in the stampede but the death toll crept up over the weekend, and the religious affairs ministry confirmed Monday that it now stood at 41.

In addition, 10 Indonesians were being treated for their injuries in hospital while a further 82 remain missing, although senior ministry official Abdul Djamil said it was not clear if they were caught up in the stampede.

He said that it was taking time to work out the number of Indonesian victims as Indonesian officials were only given access to morgues two days after the stampede, and the teams were having trouble identifying bodies against their own records of pilgrims.

"This means we have to race against time because the longer we wait, the harder it is to identify the hajj pilgrims who have died," Djamil said in a statement.

Many pilgrims' bodies were mutilated in the crush, and Djamil said that officials were identifying Indonesian victims through such methods as checking clothes and hajj ID bracelets against their records.

"Our team has been working hard day and night to look for the pilgrims whose whereabouts are still unknown, and to identify the pilgrims who died," he added.

Indonesia, home to around 225 million Muslims, gets the largest annual hajj quota from Saudi Arabia, this year receiving 168,000 places. Other countries with substantial numbers of pilgrims killed in the accident include Morocco, Egypt and India.

The Saudi Arabian interior ministry said it assigned 100,000 police to secure the hajj and manage crowds at the event, which drew almost two million faithful. But pilgrims blamed the stampede on police road closures and poor crowd management in searing temperatures.

For years, the hajj was marred by stampedes and fires, but it had been largely incident-free for almost a decade after safety improvements and billions of dollars' worth of infrastructure investment.