"I met with Foreign Minister Nasser Judeh and discussed Iran's offer to provide aid to Syrian refugees in Jordan as well as on the Syrian-Lebanese border," Abdollahian told reporters in Amman.
Jordan says it is hosting more than 300,000 Syrians, while the UN High Commissioner for Refugees estimates there are 200,000 refugees in Lebanon.
The United Nations has predicted the number of Syrian refugees in neighbouring countries will double to 1.1 million by June if Syria's 22-month conflict -- which it says has killed more than 60,000 people -- does not end.
The Iranian deputy foreign minister also called for an end to the violence in Syria, where he said a national dialogue was needed to pave the way for an accepted government.
"It is the best solution," said Abdollahian, warning however against foreign interference "to impose change in Syria."
The UN refugee agency said Friday that more than 6,400 Syrian refugees had fled the country's escalating violence to Jordan's Zaatari camp in the past 24 hours, bringing to over 30,000 the number of arrivals since the start of the month.