Abdullah made the remarks in a meeting with Iranian Ambassador to Afghanistan Bahador Aminian.
Aminian voiced his satisfaction over starting peace talks between Afghanistan and Taliban.
He stressed that Iran supports sustainable peace and stability in Afghanistan.
Abdullah referred to intra-Afghan peace talks in Qatar, and appreciated Iran’s supports.
Zarif had in a phone call with Afghanistan's acting Foreign Minister Mohammad Hanif Atmar on Tuesday offered Iran's readiness for any assistance to Peace Process in Afghanistan.
He discussed the latest situation of Afghan parties within the framework of the peace process, the role of neighboring countries in it, as well as issues of mutual interest.
Expressing satisfaction with the holding of talks among the Afghan parties, he stressed Iran's readiness for any assistance to the peace process in Afghanistan.