He also said Tehran, which has backed Damascus during its 12 years of conflict, would join efforts to reconcile Syria and Turkey, which has long supported rebel groups opposed to Syrian President Bashar al-Assad.
Assad has been politically isolated in the region since the start of Syria's war in 2011, triggered by the government's suppression of pro-democracy demonstrations, and was expelled from the Cairo-based Arab League.
But since the quake, Arab leaders have made overtures to his government.
"We welcome the recent opening of Syrian relations with some countries," Iranian Foreign Minister Hossein Amir-Abdollahian said during a press conference with his Syrian counterpart, according to an Arabic translation provided at the event.
Late last month Egypt's foreign minister became the third top Arab diplomat to meet Assad since the February 6 quake killed more than 50,000 people in total, with nearly 6,000 dead in Syria.
Assad has also received calls and earthquake aid, which has been spearhead by the United Arab Emirates.
Analysts say Syria's isolated government could leverage this momentum to bolster regional support.
Amir-Abdollahian landed on Thursday in quake-wracked Latakia province before flying to the Syrian capital, Damascus, where he met Syrian Foreign Minister Faisal Mekdad as well as Assad.
He discussed with Assad "Iran joining meetings to build a dialogue between Damascus and Ankara," the Syrian presidency said.
He also said Iran "expressed satisfaction with the path of rapprochement between Syria and Arab countries," according to the presidency statement quoting Amir-Abdollahian.
With Russian and Iranian support, Damascus has clawed back much of the ground lost in the early stages of the war.
In late December, Syrian and Turkish defence ministers held talks in Moscow -- the first such meeting since Syria's war began.
Assad had in January said a Russian-brokered rapprochement with Turkey should aim for "the end of occupation" by Ankara of parts of Syria.
The mooted reconciliation has alarmed Syrian opposition leaders and supporters who reside mostly in parts of the country under Ankara's indirect control.
The foreign minister of Saudi Arabia, which has also sent quake aid to Syria, said last month that a consensus was building in the Arab world that a new approach requiring negotiations with Damascus would be needed to address humanitarian crises including the quake.
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