During the phone conversation, the two sides exchanged views on the UN plan for the establishment of ceasefire in the war-torn country and also the measures to start political dialogue among Yemeni groups.
Amir Abdollahian underlined the necessity for immediate end to foreign military aggression against Yemen and to the ongoing siege on the country.
He said foreign military aggression has destroyed infrastructures in Yemen and resulted in the death of innocent people.
The deputy foreign minister lauded the constructive efforts made by the UN secretary general and his envoy to Yemen, and asked for more active contribution of the United Nations to restore peace in the war-torn Arab state.
Amir Abdollahian further said Iran is in constant consultations with the UN chief representative and supports any efforts for successful real talks and a fair result.
The UN envoy, for his part, appreciated Iran's efforts to help find a way out of the Yemeni crisis.
Pointing to his talks with the two conflicting Yemeni parties, Sheikh Ahmed said a draft political deal has been introduced and the Yemeni groups will declared their views on it in coming days.