"The nation of Iran will remain alongside the Syrian nation in fighting terrorism and safeguarding Syria's territorial integrity," Rouhani said in the call on Saturday evening, according to a statement on the presidency website.
He said Western allegations that Assad's regime was behind a chemical weapons attack last week were "baseless" and suggested it was carried out by rebel groups to influence global public opinion.
"Terrorists must not be allowed to use such weapons to accuse others and pave the way for actions that are contrary to international law," said Rouhani.
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Assad said the US missile strikes on a Syrian air base, launched in response to the chemical weapons attack, only made him more determined.
"The United States failed to achieve its goal with this aggression, which was to raise the morale of the terrorist groups it supports after the victories achieved by the Syrian army," Assad told Rouhani, according to Syrian state news agency SANA.
"The Syrian people and army are determined to crush terrorism in every part of Syrian territory."
Iran and Russia have been the key backers of Assad and refer to all Syrian opposition groups as "terrorists".
"Greater coordination between Iran, Syria and Russia can be very effective in the fight against terrorism. Those who think that by supporting terrorists, they can change Syria's future in their interest, are absolutely wrong," Rouhani said.