A Saudi prince has called for a regime change in Riyadh after claiming poor leadership will lead the country to 'disaster' as anger continues to grow over the Hajj tragedy.

The senior prince, who has remained anonymous but is a grandson of the state's founder, Abdulaziz Ibn Saud, said there is discontent among the royal family over the leadership skills of King Salman.

He has written two letters calling for the king - who acceded the throne in January - to be removed, claiming he is 'not in a stable condition'.

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A senior prince, who has remained anonymous but is a grandson of the state's founder, Abdulaziz Ibn Saud, claims there is discontent among the royal family and public over the leadership skills of King Salman (above)

In one of the letters, published by The Guardian, he said: 'In reality the son of the king [Mohammed bin Salman] is ruling the kingdom.

'So four or possibly five of my uncles will meet soon to discuss the letters. They are making a plan with a lot of nephews and that will open the door. A lot of the second generation is very anxious.

'The public are also pushing this very hard, all kinds of people, tribal leaders. They say you have to do this or the country will go to disaster.'

The letters, written in Arabic, call for an overthrow of King Salman bin Abdulaziz al-Saud and for the 13 surviving sons of Ibn Saud to remove the leadership in a palace coup.

'Allow the oldest and most capable to take over the affairs of the state, let the new king and crown prince take allegiance from all, and cancel the strange, new rank of second deputy premier,' one letter adds.

It comes as the country continues to mourn the loss of more than 800 people after two tragedies struck Mecca.

At least 769 people were crushed to death and hundreds of others hurt in a stampede of pilgrims in one of the worst incidents in years to hit the Muslim Hajj last week.

There are calls for King Salman bin Abdulaziz al-Saud - who acceded the throne in January - to be removed over claims he is 'not in a stable condition'

The tragedy struck during a morning surge of pilgrims at the intersection of streets 204 and 223 as the faithful were making their way toward a large structure overlooking the columns, according to the civil defence directorate.

The stampede came just two weeks after a construction crane collapsed at Mecca's Grand Mosque, Islam's holiest site, killing 109 people.

Earlier today, Iranian President Hassan Rouhani accused Saudi Arabia of incompetence over the deadly Hajj stampede and demanded an investigation of the disaster.

In his address to the UN General Assembly, he said the pilgrims were taking part in a 'grand and global spiritual gathering of the Hajj' but 'fell victim to the incompetence and mismanagement of those in charge'.

He also used the podium to lash out at Saudi authorities, saying that 'due to their unaccountability, even the missing cannot be identified and the expeditious return of the bodies of the deceased to their mourning families has been prevented.'

Iran has been deeply critical of Saudi Arabia over the tragedy, accusing its regional rival of serious safety lapses.

The Iranian president was to cut short his visit to New York and return to Tehran after his address to attend a repatriation ceremony for the bodies of the victims.

Rouhani urged Riyadh to allow immediate consular access to quickly identify the bodies and ensure their return home.

He called for 'an independent and precise investigation into the causes of this disaster and ways of preventing its repetition in the future.'

The Hajj drew some two million pilgrims from 180 countries this year, though in previous years it has drawn more than three million without any major incidents.

Questions over the leadership of King Salman come as the country continues to mourn the loss of more than 800 people after two tragedies struck Mecca. Pictured: Bodies lined up in Mina after a stampede killed 769

At least 769 people were crushed to death and hundreds more hurt in a stampede at the Muslim Hajj last week. Two weeks prior, more than 100 people were killed when a crane crashed into the Grand Mosque (pictured)

Muslims are required to perform the five-day pilgrimage once in their lifetime, and each year poses a massive logistical challenge for the kingdom.

This year also marked the first Hajj overseen by King Salman, who holds the title of 'custodian of the two holy mosques,' which gives the monarchy great religious clout and prestige in the Muslim world.

The remarks by Rouhani came amid ongoing tensions between Iran and Saudi Arabia over the conflicts in Yemen and Syria.

King Salman is pushing for Sunni Muslim Middle East countries to set aside differences over political Islam and focus on what it sees as the more urgent threat from Tehran.

Riyadh views Tehran as trying to use them to expand its influence in the region.

The wars in Syria and Yemen are among the key issues to be discussed during the UN General Assembly debate.

Rouhani was making his first visit to the United Nations since the nuclear accord was reached with the so-called P5+1 - Britain, China, France, Russia, the United States, plus Germany.