Amirabdollahian made the remarks in a phone call with UN Secretary General Antonio Guterres.
Both sides reviewed regional and international issues, including developments in Afghanistan and nuclear talks in Vienna.
Amirabdollahian called on other parties to comply with their commitments under the nuclear deal, also known as the Joint Comprehensive Plan of Action (JCPOA), saying Iran will then stop its remedial measures.
He stressed that any agreement should be verifiable.
He hailed Iran's constructive talks with the IAEA Chief Rafael Grossi in Tehran, saying Tehran will continue technical cooperation with the IAA.
Guterres, for his part, welcomed resuming Vienna talks and hoped for the negotiation to bear fruit.
He also said that Iran's request about verifiability of the removal of sanctions was logical.
He also stressed UN's all-out support for the revival of the deal.
Guterres referred to the efforts for injecting liquidity to Afghanistan's economy by establishing an international monetary fund.
