During the meeting, Qalibaf and Abdullah conferred on bilateral ties between the two neighboring states as well as the latest developments in Afghanistan and the peace talks.
Abdullah arrived in Tehran on Sunday for a three-day stay and meeting with a host of officials, including President Hassan Rouhani and Foreign Minister Mohammad Javad Zarif.
Before this trip, Abdullah also visited Pakistan and India where he discussed the Afghan peace process with those countries' senior officials.
His trip comes amid ongoing peace negotiations between delegates from the Islamic Republic of Afghanistan and the Taliban.
Zarif in a meeting with Abdullah on Sunday underscored his country’s support for peace talks and process led by the Afghans.
During the meeting in Tehran, Zarif reiterated Iran’s support for the Afghan government and the peace process led and managed by the Afghans and agreements of participants in intra-Afghan talks.
He also appreciated Abdullah for his partnership in the political process of Afghanistan, stressing Iran’s support for Taliban’s partnership in the political structure of the country.
Abdullah, for his part, elaborated on the latest developments in Afghanistan and the intra-Afghan talks.
Iranian Foreign Ministry Spokesman Saeed Khatibzadeh wrote in a tweet on Sunday that "independent, developed and with peace and stability Afghanistan has always been the desire of Iran”.
"We will do our best to help the genuine Afghan-Afghan dialogue," he said.