Iranian state news agency Irna said 530 people had died in Iran alone.
Tuesday has been declared a national day of mourning in Iran for hundreds of people killed in Sunday's natural disaster that also devastated parts of bordering Iraq.
Maj Gen Mohammad Ali Jafari, head of the elite Islamic Revolutionary Guards Corps (IRGC), said that the immediate needs were tents, water and food.
On Tuesday, Iran marked a day of mourning, with a black banner adorning the corner of images of the disaster broadcast by state television.
Rouhani Tuesday visited the town of Sar-e Pol-e Zahab, worst hit by the quake.
About 30 Red Crescent teams were working in the natural disaster zone.
Competing in the men's 85-kilogram weight category, Rostami became the first Iranian to take home gold in the 2016 Olympics, lifting a world record 396 kilograms from the ground to his shoulders, regaining his strength and composure before hoisting it above his head.
So far, rescue operation and assessment is being conducted on the ground and relief items including tents, ground sheets, blankets, kitchen sets, and food items such as canned food and rice are being distributed among the affected people and the people staying outdoor, scaring of getting back to their houses.
An estimated 70,000 people living close to the Iran-Iraq border have been made homeless and the government is struggling to get aid to those in need.