"There can't be any discussion on prolonging Russia's membership in the FAO," Zelensky told delegates at a Paris meeting of the Organization for Economic Co-operation and Development (OECD) by video link.
"What is there for Russia to do (in the FAO) if they are causing hunger for at least 400 million, or potentially more than a billion people?" Zelensky added.
Ukraine's Black Sea ports usually export millions of tons of grain each year but have been blocked since Moscow's late February invasion.
Along with western sanctions on Russia, which prevent Moscow selling much of its grain abroad, the blockade has sent food prices soaring and triggered warnings of famine in the Middle East and Africa.
Russian Foreign Minister Sergei Lavrov claimed at UN-backed talks in Turkey on Wednesday that Moscow was ready to grant safe passage to ships transporting Ukrainian corn and wheat.
Ukraine says it is open to resuming shipments but needs concrete security guarantees from Russia, an FAO member since 2006.
Active in 130 countries worldwide, the FAO's mission is to "achieve food security for all".
"The United Nations' mediation efforts are significant steps, and I think, unfortunately, the only ones," Italian Prime Minister Mario Draghi told Thursday's OECD meeting.
"We have to offer President Zelensky the assurances he needs that the ports will not be attacked."