In his message released on Tuesday, Rouhani expressed deep grief on the sad occasion of Ayatollah Shahroudi's death.
He also referred to Shahroudi's attempts to promote the Islamic-Iranian culture and civilization, to reinforce the relations between seminaries and universities and to develop human sciences.
Rouhani condoled with the family of the late Ayatollah.
After a long battle with disease, Ayatollah Shahroudi succumbed to death, on Monday evening at the age of 70.
Shahroudi was born in Najaf, Iraq, in 1948 and had served as a member of the Guardian Council as of 1994.
He was also judiciary chief and member of Experts Council. As of 2017, he was chairman of Expediency Council.