During the telephone conversation Larijani said Iran believes that Yemen's crisis should be resolved through national dialogue among all Yemeni political factions.
Mr. Rouhani also appealed to Iraq and international institutions to try their best to end the aggression and send humanitarian aid to the stricken country.
The protesters gathered outside the Saudi embassy in Tehran, chanting slogans against Saudi Arabia, the US and Israel.
Iran’s Foreign Ministry Spokeswoman Marzieh Afkham congratulated the Iraqi army and popular and tribal forces for their courageous victory in Salahuddin province.
Iran’s deputy foreign minister said that the Saudi military intervention in Yemen is a strategic mistake and won’t help solve Yemen’s problems.
Hossein Mozafar said the Ministry of Foreign Affairs should act more decisively and call off Erdogan’s Tehran visit unless he apologizes for what he has said.
In insulting comments, the Turkish president said Iranian MPs protesting against his comments about Iran’s role in Yemen are out of their league.
Afkham denounced allegations about Iran sending weapons to Yemen as “complete fabrications” and “sheer lies”.
Deputy Foreign Minister Hassan Ghashghavi said the solution to the problems of Yemen does not go through foreign intervention or military aggression.
Rafsanjani, who is known to have had very good relations with senior Saudi officials when he was Iran's president, has voiced deep concern over the ongoing crisis in Yemen.