Smoke rises from an oil refinery in Lysychansk about 120km north of Donetsk. AFP

The General Staff of Ukraine's armed forces also reported Russian shelling of more than a dozen towns on the southern front — particularly the Kherson region, mainly controlled by Russian forces, but where Ukrainian troops are steadily capturing territory.

Much attention has been focused on the Zaporizhzhia nuclear plant in southern Ukraine amid fears of a catastrophe over renewed shelling in recent days that Russia and Ukraine blame on each other.

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Heavy fighting near Donetsk as Russia presses offensive in eastern Ukraine

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UN Secretary-General Antonio Guterres has called for the establishment of a demilitarised zone and Ukrainian President Volodymyr Zelensky has warned Russian soldiers who shoot at Europe's largest nuclear power station or use it as a base to shoot from that they will become a "special target" of Ukrainian forces.

The Zaporizhzhia plant dominates the south bank of a vast reservoir on the Dnipro River. Ukrainian forces controlling the towns and cities on the opposite bank have come under intense bombardment from the Russian-held side.

Service members of pro-Russian troops stand guard in the southern port city of Mariupol, Ukraine. File/Reuters

The International Atomic Energy Agency, which seeks to inspect the plant, has warned of a nuclear disaster unless fighting stops. Nuclear experts fear fighting might damage the plant's spent fuel pools or reactors.

Zelenskiy said Ukraine had many times proposed different formats to the Russian leadership for peace talks, without progress.

"So we have to defend ourselves, we have to answer every form of terror, every instance of shelling - the fierce shelling which does not let up for a single day," he said in video remarks late on Sunday.

Fighting in East, South

Kyiv has said for weeks it is planning a counteroffensive to recapture Zaporizhzhia and neighbouring Kherson province, the largest part of the territory Russia seized after its Feb. 24 invasion and still holds.

Ukraine's military command said early on Sunday that Russian soldiers had continued unsuccessfully to attack Ukrainian positions near Avdiivka, which, since 2014, has become one of the outposts of Ukrainian forces near Donetsk.

People watch smoke rising behind buildings following explosions in Lviv, Ukraine. File/AP

Ukrainian military expert Oleg Zhdanov said the situation was particularly difficult in Avdiivka and nearby towns, such as Pisky.

"We have insufficient artillery power in place and our forces are asking for more support to defend Pisky," he said in a video posted online. "But the town is basically under Ukrainian control."

Grain ships

Amid the fighting, more ships carrying Ukrainian grain left or prepared to do so as part of a deal struck late last month to ease a global food crisis.

The Fulmar S vessel carrier with 12,000 ton of corn makes its way from the port in Odesa, Ukraine, on Saturday. AP

An Ethiopia-bound cargo, the first since Russia's invasion of Ukraine, was getting ready to leave in the next few days, while sources said the first grain ship to leave Ukraine under a UN deal was nearing Syria.

"The world needs the food of Ukraine," Marianne Ward, the deputy country director of the World Food Programme, told reporters. "This is the beginning of what we hope are normal operations for the hungry people of the world."

Reuters