International Atomic Energy Agency (IAEA) director general Rafael Grossi this week urged Moscow and Kyiv to allow experts to visit the site, Europe's largest nuclear power plant, and stabilise the situation to avoid a nuclear accident.
Russian troops seized the plant in early March, shortly after their invasion of Ukraine began on February 24.
Moscow says it has put together a proposal to facilitate the visit but that the UN turned down the offer.
"We were prepared to assist the International Atomic Energy Agency in organising an international mission headed by the Director General to assess the situation of this largest nuclear power plant on the territory of Europe," said Igor Vishnevetsky, deputy director of the Russian Non-proliferation and Arms Control Department, according to state-owned media.
"We came to an agreement regarding the timeline of the visits, the very complex logistics, as well as security arrangements. However, just days before the proposed arrival of the IAEA delegation, the Secretariat of the United Nations refused to approve this visit."
There has been no confirmation from the UN that it rejected the proposal.
“Every principle of nuclear safety has been violated [at the plant]", Mr Grossi told AP on Tuesday. "What is at stake is extremely serious and extremely grave and dangerous.”
But he has said there are significant challenges in visiting the site, which he described as being in the "paradoxical situation" of being owned and operated by Ukraine within the country's territory but in the hands of Russia.
The IAEA has faulty and patchy contact with employees at the plant, Mr Grossi said.
"Going there is a very, very complicated thing because it requires the understanding and co-operation of a number of actors," he said on Wednesday.
"Of course, it's a Ukrainian facility so it requires Ukraine to agree with it, be comfortable with it and help me carry out the mission.
"At the same time, the plant is occupied by Russia and I have to talk to everybody and especially those who are in control of the place in fulfilling my technical duty."
The supply chain of the equipment and spare parts at the site has been interrupted, “so we are not sure the plant is getting all it needs," he said.
There is a lot of nuclear material in need of inspection, he said.
“When you put this together, you have a catalogue of things that should never be happening in any nuclear facility,” Mr Grossi said.
“And this is why I have been insisting from day one that we have to be able to go there to perform this safety and security evaluation, to do the repairs and to assist as we already did in Chernobyl."
The Russian capture of Zaporizhzhia sparked fears that the largest of Ukraine’s 15 nuclear reactors could be damaged, setting off another emergency like the 1986 Chernobyl accident, the world’s worst nuclear disaster, which happened about 110 kilometres north of Kyiv.
Russian forces occupied the heavily contaminated Chernobyl site soon after the invasion began but handed control back to the Ukrainians at the end of March.
Mr Grossi visited Chernobyl on April 27 and tweeted that the level of safety was “like a 'red light’ blinking," but said later that the IAEA had set up “an assistance mission ... that has been very, very successful so far".
The IAEA needs to go to Zaporizhzhia to ascertain what is actually happening there, to carry out repairs and inspections, and “prevent a nuclear accident from happening", Mr Grossi said.