Saudi Arabia, under growing pressure to account for a stampede that killed more than 700 people at the hajj pilgrimage near Mecca on Thursday, has suggested that pilgrims failing to follow crowd control rules bore some of the blame for the worst disaster at the event in 25 years.

Other countries strongly rejected those claims, however, with Saudi's regional rival Iran in particular describing Riyadh's "incompetence." Nigeria and Pakistan also dismissed the Saudi remarks.

In a statement posted on his ministry's website, Saudi Health Minister Khalid al-Falih said an investigation would be conducted rapidly and a final toll of dead and wounded soon calculated. At least 863 pilgrims were injured in the tragedy, according to the most recent figures.

"The investigations into the incident of the stampede... which was perhaps because some pilgrims moved without following instructions by the relevant authorities, will be fast and will be announced as has happened in other incidents," the statement said.

Falih also said the hundreds of injured were being transferred to hospitals in Mecca, and if necessary to other parts of the kingdom.

Falih's comments were likely to be seen by the kingdom's critics as an attempt to deflect responsibility for the incident: Safety during hajj is politically sensitive for the kingdom's ruling Al Saud dynasty, as the ruling family presents itself internationally as the guardian of orthodox Islam and custodian of its holiest places in Mecca and Medina.

With photographs of piles of the dead circulating on social media and pilgrims frantically searching for missing compatriots, the effort to uncover the facts and assign blame will likely to grow more acute and possibly more political.

Saudi King Salman also ordered a review of hajj plans after the disaster, in which two big groups of pilgrims collided at a crossroads in Mina, a few miles east of Mecca, on their way to performing the "stoning of the devil" ritual at Jamarat.

Iran, meanwhile, expressed indignation at the deaths of 131 of its nationals at the world's largest annual gathering of people, and politicians in Tehran suggested Riyadh was incapable of managing the event.

Iran's President Hassan Rouhani, in New York to attend the UN General Assembly, echoed the Supreme Leader Ayatollah Ali Khamenei in blaming Saudi Arabia for the incident.

"I ask the Saudi Arabian government to take the responsibility of this catastrophe and fulfil its legal and Islamic duties in this regard," Rouhani said in a statement published on the state news agency IRNA.

In Tehran, protesters held a demonstration after Friday noon prayers. Iranian state television said they were showing their anger at "Saudi incapability and incompetence to run the hajj."

Hamid Aboutalebi, Rouhani's deputy chief of staff, was also quoted by Fars news agency as saying "the incompetence of Saudi Arabian government in this incident in obvious."

Iran's deputy Foreign Minister, Hossein Amir Abdollahian called "Riyadh's negligence inexcusable" and announced a committee has been established to look into the incident.

Iranian pilgrims who survived the deadly incident described Saudi's response "too little, too late," according to Iran's state run Press TV. They said the rescuers arrived at the scene two hours after the incident and started collecting dead bodies first instead of helping the injured.

Saudi Arabia's Interior Ministry spokesman Major General Mansour Turki was quoted in Saudi media on Friday as saying the security forces had immediately responded and begun to rescue those who fell in the crush.

"This year hajj ceremony was disorganised as Saudi government had hired young and inexperienced people," Saeed Ohadi, head of Iran's hajj and pilgrimage organization told Iran's state broadcaster in a live interview from Mecca.

A leading Iranian MP said Saudi Arabia is not qualified to be in charge of Hajj. "The fatal stampede occurred after Saudi officials closed two routes leading to site ritual," Alaeddin Boroujerdi, head of parliament's Foreign Affairs and National Security committee was quoted as saying by Fars news agency.

Speaking in New York, Pope Francis expressed "sentiments of closeness" with the world's Muslims after the tragedy. UN Secretary General Ban Ki-moon and the United States also offered condolence.

In Islamabad, the Pakistani ministry of religious affairs said seven Pakistanis were dead and six were injured.

Former Iraqi Prime minister Nuri al-Maliki, an ally of Iran and foe of Riyadh, said the incident was "proof of the incompetence of the organizers of the pilgrimage season".

He said the hajj should be placed under the authority of the Organization of the Islamic Conference, the world's largest Muslim organisation.