0246 GMT May 21, 2018
Rouhani, who visited the western province of Kermanshah said the government would would move swiftly to help those left homeless by the disaster.
"I want to assure those who are suffering that the government has begun to act with all means at its disposal and is scrambling to resolve this problem as quickly as possible," he said.
The 7.3-magnitude tremor, Iran’s deadliest earthquake in more than a decade, killed at least 530 people and injured more than 8,000 others in Kermanshah province, according to IRNA.
On Tuesday, residents who had fled their homes awoke from a second night in the cold outdoors as authorities struggled to get aid into the quake zone.
Rouhani said the government plans to support reconstruction with both handouts and loans. He assured the injured and those who have lost their homes and possessions that the government will stand by them and do its best to help them.
The Iranian Army, the Islamic Revolution Guards Corps (IRGC), the Basij volunteer force, the Red Crescent as well as the ministries of energy, interior, health, and roads and urban development were all providing assistance, he added.
Rouhani said all aid would be channeled through the Housing Foundation, one of the charitable trusts set up after the 1979 Islamic Revolution.
He appreciated foreign countries for expressing sympathy with victims of Sunday's temblor.
The latest message of condolence was issued on Tuesday by Japanese Prime Minister Shinzo Abe who said he was heartbroken at the news of the deadly quake.
While touring Sarpol-e Zahab town, Rouhani said the government will probe the cause of so much damage to buildings constructed under a state-owned program in the quake-stricken area by the former administration.
The worst damage appeared to be in Sarpol-e-Zahab.
At least 280 people were killed in the town, home to some 85,000 people, where crumpled vehicles lay under the rubble of flattened buildings on the streets.
Rouhani pledged the "government will definitely follow up on these issues and identify the culprits."
Many of the damaged buildings were built during former president Mahmoud Ahmadinejad’s government, though some of them were completed and handed over to the residents under Rouhani.
Rouhani said that "the faults and shortcomings in the construction of these buildings should be investigated".
Under the plan dubbed Mehr, or "kindness" in Persian, some 2 million units were built in Iran, including hundreds in Sarpol-e Zahab.
People in urgent need
Around 12,000 Iranian homes were destroyed and another 15,000 damaged in the quake, according to official estimates. Local reports said many people were still in need of tents and blankets.
IRGC Commander Major General Mohammad Ali Jafari said the immediate need was for tents, water and food.
"Newly constructed buildings... held up well, but the old houses built with earth were totally destroyed," he told Iranian television as he visited the affected region.
Seven towns and nearly 2,000 villages were damaged, authorities said, and several villages were completely wiped from the map.
On Tuesday, Iran marked a day of mourning, with a black banner adorning the corner of images of the disaster broadcast by national television.
"The most urgent need is to provide solutions for heating, housing and food," Pir Hossein Koolivand, the head of national rescue services, said.
"Today, we sent our ambulances to villages in areas affected by the quake to help people rescued yesterday, including changing their bandages," he said.
He added that "psychological support teams" have been sent to these areas.
The authorities said water and electricity had returned to most affected regions.
On Monday, officials said they were setting up relief camps for the displaced and that 22,000 tents, 52,000 blankets and tons of food and water had been distributed.
Hundreds of ambulances and dozens of army helicopters joined the rescue effort after Iran’s Leader Ayatollah Seyyed Ali Khamenei ordered the government and armed forces to mobilize "all their means".
By late Monday, officials said all the roads in Kermanshah province had been reopened.
Sunday's quake struck along a 1,500-kilometer fault line between the Arabian and Eurasian tectonic plates, which extends through western Iran and northeastern Iraq. The area sees frequent seismic activity.
In 1990, a 7.4-magnitude quake in northern Iran killed 40,000 people, injured 300,000 and left half a million homeless, reducing dozens of towns and nearly 2,000 villages to rubble.
Thirteen years later, a catastrophic quake flattened swathes of the ancient southeastern Iranian city of Bam, killing at least 31,000.
Iran has experienced at least two major quake disasters since – one in 2005 that killed more than 600 people and another in 2012 that left some 300 dead.
AFP, AP, Reuters and Press TV contributed to this story.