Four more ships loaded with grain set off from Ukrainian ports on Sunday, as Moscow and Kyiv blamed each other for a new strike at a Russian-occupied nuclear plant.

Odessa regional authorities, meanwhile, announced that another two grain shipments were due to leave on Monday.

Kyiv's infrastructure ministry wrote on Telegram on Sunday that a convoy of Ukrainian supplies had left, with three ships departing from Chornomorsk and one from Odessa.

The Mustafa Necati, the Star Helena, the Glory and the Riva Wind were carrying "around 170,000 tonnes of agriculture-related merchandise", it said.

The spokesman for the Odessa regional military administration said early Monday morning that the MV Sacura and MV Arizona had also been cleared to set sail.

It would "transport more than 59,000 tonnes of food via the maritime humanitarian corridor today", he said.

Moscow and Kyiv traded accusations on Sunday over who bombed the Zaporizhzhia nuclear site in southern Ukraine.

Europe's largest atomic power complex has been under Russian control since the early days of the February 24 invasion.

Recent fighting at the plant has prompted the UN's nuclear watchdog, the International Atomic Energy Agency (IAEA), to warn of "the very real risk of a nuclear disaster".

Russia's occupying authorities in the town of Enerhodar, where the plant is located, said the Ukrainian army overnight "carried out a strike with a cluster bomb fired from an Uragan multiple rocket launcher".

The projectiles fell "within 400 metres of a working reactor" and in a "zone storing used nuclear fuel", Russia's state news agency TASS reported.

Ukrainian state nuclear energy company Enerhoatom, however, said the "Russian occupiers once again fired rockets at the nuclear power plant (and) its host town, Enerhodar". One worker there had been hospitalised with shrapnel wounds, it added.

AFP was not able to confirm the allegations from an independent source.

Without assigning blame, United Nations Secretary-General Antonio Guterres condemned the strike in remarks from Tokyo on Monday morning.

"Any attack to a nuclear plant is a suicidal thing. I hope that those attacks will end, and at the same time I hope that the IAEA will be able to access the plant," he said.

On Saturday, Enerhoatom had already said parts of the facility had been "seriously damaged" by military strikes the previous day, forcing the shutdown of one of its reactors.

Ukraine President Volodymyr Zelensky in his nightly address Sunday, called for a "principled response" from the international community.

Evoking the possibility that the plant was hit causing the release of a toxic cloud, he added: "No one will stop the wind that will spread the radioactive contamination."

Amnesty International on Sunday said it deeply regretted the "distress and anger" caused after it alleged Ukrainian forces were flouting international law by exposing civilians to Russian fire, but stood by its controversial report.

The Thursday report, which sparked outrage in Ukraine, accused the military of endangering civilians by establishing bases in schools and hospitals, and launching counter-attacks from heavily populated areas.

Meanwhile, the renewed shipments of Ukrainian grain to help ease global food shortages and bring down prices offered a small glimmer of hope as the war entered its sixth month.

Ukraine, one of the world's largest grain exporters, had been forced to halt almost all deliveries in the wake of Russia's invasion.

That sent global food prices soaring, making imports prohibitively expensive for some of the world's poorest nations.

A bulk carrier arrived in Chornomorsk on Saturday to be loaded with grain for the first time since Moscow's invasion.

The departure Sunday of the four other vessels, along with Monday's planned departure of two more, came after several others set sail last week under a deal brokered with the help of Turkey.

In Rome on Sunday, Pope Francis welcomed the resumption of grain exports as "a sign of hope" that showed dialogue was possible to end the war.

Sunday also saw Zelensky post photos of himself meeting with Oscar-winning US actress Jessica Chastain in Ukraine, just as Moscow was celebrating the re-election of a former senior Russian politician to the world body governing chess.

On Telegram Zelensky underlined the value of visits from famous people, writing: "Thanks to this, the world will hear, know and understand the truth about what is happening in our country even more."

Earlier on Sunday, Moscow had celebrated a diplomatic victory of its own with the re-election of Russia's Arkady Dvorkovich to the helm of the international chess body FIDE.