ABU DHABI: Saudi Prince Turki al-Faisal on Sunday rejected the idea of sharing the administration of the annual Haj pilgrimage with other Muslim nations, saying Riyadh considers it "a matter of sovereignty" and a "privilege."

The senior member of the Saudi royal family spoke to The Associated Press (AP) as his country faces mounting criticism in the wake of last month's disastrous crush of pilgrims outside the holy city of Makkah, which killed over 1,400 people, according to an AP count, making it the deadliest annual pilgrimage on record.

Saudi Arabia's regional rival Iran, which lost the largest number of pilgrims, has accused the kingdom of mismanagement and called for an independent body to oversee the Haj.

Read: Iran's Khamenei demands Saudi apology for Haj deaths

The Royal Al Saud family, which governs Saudi Arabia and for which the country is named after, derives enormous prestige and legitimacy from being the caretakers of the Haj and Islam's holiest sites in Makkah and Medina.

King Salman, in line with past Saudi monarchs, holds the title of "Custodian of the Two Holy Mosques" in reference to the Grand Mosque in Makkah and the Prophet Muhammad's (PBUH) first mosque ever built in Medina.

Oversight of these holy places and the Haj "is a matter of sovereignty and privilege and service," Prince Turki said.

"The kingdom over the years, having gotten over the awful times when pilgrims couldn't guarantee their travels to the Haj in the old days and all the other factors of disease and crowds and housing and so on, we'll not give up that privilege or that distinction of being the servants of the two holy places," he said.

"The people of Makkah are the ones who know best the territory of Makkah and you can't take that away from the people of Makkah."

Turki is the most senior Saudi royal to comment publicly on the Iranian criticism.

He is currently chairman of the Riyadh-based King Faisal Centre for Research and Islamic Studies, named after his late father.

The prince served for more than two decades as head of intelligence in the kingdom, and has held ambassador posts in Britain, Ireland and the United States.

His brother, Prince Khalid al-Faisal is currently the governor of Makkah.

Turki spoke to the AP in an interview Sunday on the sidelines of an event in Abu Dhabi organised by the Beirut Institute think tank.

At least 1,480 pilgrims died when large crowds converged down a narrow street on September 24 in the area of Mina, just outside Makkah.

The death toll is based on an AP count from official statements from 19 nations whose citizens died in the incident.

The death toll given by Saudi Arabia's Health Ministry is 769.

Health and security officials have not immediately responded to AP requests for clarification.

Iran's death toll of 465 is the highest announced by any country thus far.

Egypt's Foreign Ministry on Sunday said the death toll among Egyptians climbed from 165 to 177, with 64 still missing.

Read: New report puts Mina stampede death toll at 1,260

As thousands of pilgrims headed down narrow streets in Mina, they converged on another large crowd, causing people to trip over one another, fall and suffocate in a chaotic crush that lasted for more than an hour, according to survivors.

The street where the crush took place is surrounded by iron gates, behind which are tents for pilgrims. The tragedy took place around 1.6 kilometres from a multi-million dollar facility built by the Saudi government to ease congestion and deadly accidents during a ritual where Muslims throw pebbles at three columns in a symbolic stoning of the devil.

The pilgrimage, which all able-bodied Muslims are required to perform once in a lifetime, is a chance for believers to wipe away past sins.

The Jamarat complex in Mina is an example of the many projects the kingdom has undertaken to make the pilgrimage safer.

Saudi Arabia has spent billions of dollars and undertaken massive construction projects to ease the Haj for the world's Muslims, and the last serious loss of life had occurred nine years ago.

This year, the Haj drew around 2 million people from more than 180 countries to Islam's holiest site in Makkah, the cube-shaped Kaaba to which Muslims around the world pray toward and circle during pilgrimages.

Within hours of the stampede, Iran's Supreme Leader Ayatollah Ali Khamenei had accused Saudi Arabia of "mismanagement."

Iran's President Hassan Rouhani suggested "ineptitude" on the part of Saudi authorities.

Scores of Iranians protested against the kingdom outside the Saudi Embassy in Tehran, and Iranian lawmakers and clerics called on the Organization of Islamic Cooperation (OIC) to manage the haj.

Iran's state prosecutor has vowed to "pursue the trial of Al Saud" through international courts for the deaths in this year's Haj.

"I think they're trying to make political capital out of this, which is unfortunate," Turki said, adding that "human suffering should not be a tool for political shenanigans."

"It's a recurring record that is played over and over again by Iranian leaders."

Saudi plans tripling of Umrah visas: reports

Saudi Arabia is planning to triple the number of visas it issues for Umrah, reports said on Monday, less than three weeks after the deadly stampede at Mina during this year's Haj.

The Saudi Gazette and Okaz newspapers quoted Haj Minister Bandar al-Hajjar as saying that as many as 1.25 million pilgrims are expected to arrive each month starting next year. That compares with 400,000 a month now, the reports said.

Hajjar was quoted as saying the new system would allow full use of massive expansion projects at the kingdom's holy sites.

This year's Haj drew about 2m Muslim pilgrims. The number had declined, particularly because of a multi-billion-dollar expansion which began four years ago at the Grand Mosque in Makkah.

The 4.3-million-square-feet Grand Mosque enlargement is the equivalent of more than 50 football pitches, and it will allow the complex to accommodate roughly 2m people at once.

A crane working on the expansion collapsed into a courtyard of the mosque on September 11, killing at least 108 people, including foreign pilgrims, just before Haj.

An even greater tragedy, the worst ever in the history of the pilgrimage, was the September 24 stampede during the ritual stoning of the devil at Mina. A formal Saudi inquiry is under way into the stampede.

Also read: Witnesses blame Saudi officials for Haj horror