UNITED NATIONS (Reuters) - Iranian President Hassan Rouhani used a major United Nations speech on Saturday to demand an investigation into a crush that killed more than 700 people at the annual hajj pilgrimage in Saudi Arabia.

The fact that Rouhani used a U.N. summit meeting on global development goals to reiterate Iran's outrage over the hajj tragedy was a sign that Tehran does not intend to tone down criticism of its regional rival Saudi Arabia. Both Iran and the Saudis see themselves as leaders in the Muslim world.

In his speech to the 193-nation U.N. General Assembly, Rouhani emphasized the need for an investigation into "the causes of this incident and other similar incidents in this year's hajj." He described the crush as "heart-rending."

Saudi Arabia suggested on Friday pilgrims who ignored crowd control rules bore some blame for the incident. Saudi King Salman ordered a review of hajj plans, and Health Minister Khalid al-Falih said an investigation would be conducted.

Iran has repeatedly voiced outrage at the deaths of 131 of its nationals at the world's largest annual gathering of people.

Saudi Foreign Minister Adel al-Jubeir accused Iran of playing politics with the tragedy.

"This is not a situation with which to play politics," he said before meeting U.S. Secretary of State John Kerry. "I would hope that the Iranian leaders would be more sensible and more thoughtful with regards to those who perished in this tragedy and wait until we see the results of the investigation."

Rouhani suggested on Friday the tragedy may be a result of the Saudis transferring experienced troops to Yemen to fight Iranian-backed Houthi rebels, a military campaign that Tehran has repeatedly criticized.

Two weeks ago, 110 people died in Mecca's Grand Mosque when a crane working on an expansion project collapsed during a storm and toppled off the roof into the main courtyard, crushing pilgrims underneath.

Rouhani also told the U.N. summit on Saturday that the historic nuclear deal between Iran and the United States, Britain, France, Germany, Russia and China "has created suitable conditions for regional and international cooperation including in the field of environmental preservation."

(Reporting by Michelle Nichols, Parisa Hafezi and Arshad Mohammed; Editing by Dominic Evans and Paul Tait)