Ukrainian forces reported heavy Russian shelling and attempts to advance on several towns in the eastern region of Donetsk that has become a key focus of the near six-month war, but said they had repelled many of the attacks.
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.
U.N. Secretary-General Antonio Guterres has called for the establishment of a demilitarised zone and Ukrainian President Volodymyr Zelenskiy 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. read more
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.
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. read more
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."
In the neighbouring Russian-occupied region of Luhansk, in the grounds below an abandoned, charred apartment block, Lilia Ai-Talatini, 48, watched on as her mother's body was exhumed from a makeshift grave to be taken to a cemetery for a proper burial.
Ai-Talatini told Reuters how it had taken her 10 days to reach her parents' apartment, which was on the Russian held-side of the town of Rubizhne, during heavy fighting there in March.
"Mother was already dying ... her hands were blue, her complexion was sallow, there were circles under her eyes," she said. "The next day mother passed away."
An official with the Luhansk People's Republic, a statelet set up by pro-Moscow separatists, said a team had been working in Rubizhne for 10 days and exhumed 104 sets of remains.
"It's clear that shrapnel wounds predominate, but there are also bullet wounds," Anna Soroka said, estimating there were 500 unofficial graves in the city.
Reuters could not independently verify the battlefield accounts.
Russia calls its invasion of Ukraine a "special military operation" to demilitarise and "denazify" its smaller neighbour, while Ukraine and its Western allies regard Moscow's actions as a war of aggression.
The conflict has pushed Moscow-Washington relations to a low point, with Russia warning it may sever ties.
Having been largely isolated on the global diplomatic stage, Russia has been gaining more sympathy from China, whose own ties with Washington have nosedived due to tensions over Taiwan. read more
And on Monday, North Korean state media said Russian President Vladimir Putin told leader Kim Jong Un the two countries would expand "comprehensive and constructive" ties. read more
In July, North Korea recognised as independent states the Russian-backed breakaway "people's republics" of Donetsk and Luhansk, and officials raised the prospect of its workers being sent there to help in construction and other labour.
Ukraine immediately severed ties with Pyongyang over the move.
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.
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 U.N. deal was nearing Syria. read more
"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."