Aminian also reiterated Iran's support for Afghanistan and its achievements over the past 19 years.
The Iranian and Afghan diplomats discussed issues of mutual interest including peace and political developments, Mehr News Agency (MNA) reported.
The two sides discussed issues related to strengthening Tehran-Islamabad economic, political and cultural cooperation as well as the importance of regional consensus on peace in Afghanistan, exchange of the remaining prisoners between the government of Afghanistan and the Taliban, and reducing the existing violence in that country.
Aminian further discussed the Khaf-Herat joint railway project and presented a report on the opportunities available between the two countries in expanding economic, transportation, investment and energy cooperation.
Appreciating Iran’s comprehensive cooperation with Afghanistan, especially on the issue of the Afghan immigrant citizens living in Iran, Hanif Atmar called for the continuation of bilateral cooperation.
The Taliban suspended Afghan peace talks in April over a dispute concerning the deal to release prisoners.
However, earlier in August, thousands of prominent Afghans approved to release 400 remaining Taliban prisoners whose fate has been a crucial hurdle in launching the much-delayed talks between the Taliban and the Afghan government.
At the end of a three-day "Loya Jirga" which is a traditional Afghan gathering of tribal elders, the prominent Afghans decided last Monday to release the remaining prisoners. Kabul released the first 80 of a final 400 Taliban prisoners, paving the way for negotiations, media reports said on Sunday.