The latest IAEA report concluded the destroyed facility in Syria in 2007 is a nuclear reactor.
Syria insists it is the site of military non nuclear.
United States and its allies urged that Damascus was reported to the Security Council but some countries against it.
Israel's bombardment of the facility in the desert was allegedly a reactor near Deir Alzour, Northeastern Syria in September 2007.
As much as the 35-member Board of Governors of the IAEA held a meeting during the week at the headquarters of the organization in Vienna, Austria.
In his speech to the Council, the IAEA Director General Yukiya Amano says Syria not cooperating in the case of this though has Deir Alzour given enough time.
American CIA intelligence service announced a suspected nuclear site pictures of SyriaHowever, he said, the Atomic Energy Commission has sent a letter to Syria and discussion still continues.
Amano also said penghancurkan facilities "allegedly made Israel" was "very regrettable".
"Rather than use violence case should be reported to the IAEA," he said.
BBC reporter Bethany Bell in Vienna says to a sense of frustration among the diplomats who have been trying hard ask for access to the site in Syria in three years.
However, according to a BBC journalist, diplomat, more reluctant to propose the resolution by saying Syria offers of cooperation. In addition because of unrest in Syria now may not be as teap applying pressure.
Syria is a signatory to the nuclear Non Proliferation Treaty entitles members enriched fuel for nuclear power plants under the supervision of IAEA.
But Syria is also a signatory to the nuclear safety agreement with the IAEA which oblige the country tells UN agencies if building new nuclear facilities.