In a message on Saturday, President Rouhani expressed deep sorrow at the deaths and injuries in the incident in Mecca’s Masjid al-Haram (the Grand Mosque).
On Friday evening, a large construction crane toppled over during a violent rainstorm and crashed into the mosque, killing at least 107 pilgrims and wounding 238 others.
One Iranian national was among the dead and 25 other Iranian pilgrims were injured.
Elsewhere in his message, President Rouhani expressed sympathy with the families of the victims, and wished health for the injured.
The president also voiced Iran’s readiness to give medical assistance to Saudi Arabia.
The incident has raised fears about the safety of the site before the yearly hajj pilgrimage that is expected to bring in hundreds of thousands of visitors to Saudi Arabia this month.
Masjid al-Haram is the world’s largest mosque and houses the Kaaba, the black cube that Muslims around the world pray toward and which they walk around during the pilgrimage.
The Saudi government is in the midst of a multibillion-dollar project to enlarge the mosque, and the site is currently ringed with cranes.
Large-scale deadly accidents during hajj have occurred on a number of occasions in years past.
In 2006, more than 360 pilgrims died in a stampede at the desert plain of Mina, near Mecca. A crush of pilgrims two years earlier left 244 dead.
The worst hajj-related tragedy was in 1990, when 1,426 pilgrims died in a stampede in an overcrowded pedestrian tunnel leading to holy sites in Mecca.