The visits come after several military losses for the Syrian government and as Tehran negotiates a key nuclear deal with the United States, which backs the rebels fighting Assad.
"The support given by Iran to the Syrian people constitutes a key pillar in the battle against terrorism," official news agency SANA quoted Assad as saying during a meeting with Ali Akbar Velayati, foreign affairs adviser to Iran's supreme leader.
Syria's government refers to all those seeking to oust Assad as "terrorists".
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Velayati meanwhile praised the "strategic relations" between Damascus and Tehran, saying they "constitute one of the essential pillars in confronting Western projects... and the illusions... of certain regional countries."
He said Iran would "continue to support Syria by all means," adding "a small world war is being waged against Syria," SANA said.
Velayati's visit comes after a trip by the head of a Syrian-Iranian economic commission during which several deals on electricity, industry, oil and investments were signed, SANA said.
Last Thursday, Alaedin Boroujerdi, head of the Iranian parliament's national security and foreign policy, visited Damascus and pledged Tehran's support for the regime was "firm and eternal".
Iran has remained a firm ally of Damascus throughout the uprising that began against Assad in March 2011, providing financial and military support.