A counteroffensive launched by Ukraine was reportedly making progress on Tuesday with Kyiv claiming its forces had broken through Russian lines in the port city of Kherson, a key prize in the battle for control of southern territory.
President Volodymyr Zelenskyy declared there was no place in Ukraine for Russia forces, calling on those on the front lines to "flee for their lives".
Mr Zelenskyy, in his nightly address on Monday, said Ukrainian troops would chase the Russian forces “to the border”.
“If they want to survive — it's time for the Russian military to run away. Go home,” Mr Zelenskyy said. “Ukraine is taking back its own.”
Oleksiy Arestovych, a senior adviser to Mr Zelenskyy, said Russian defences had been “broken through in a few hours”.
Ukrainian forces were shelling ferries Russia was using to supply a pocket of territory on the West bank of the Dnipro river in the Kherson region, he said. The president's office added "heavy fighting is taking place in almost the entire territory of the Kherson region".
"Powerful explosions continued throughout the day and throughout the night [as] the Armed Forces of Ukraine launched offensive actions in various directions," it added.
Russia's defence ministry claimed Ukraine suffered "large-scale losses" of more than 1,200 soldiers and dozens of pieces of equipment during the "defeat" of its southern attack.
Britain's defence ministry had given warnings that, since the start of August, Russia made "significant efforts" to reinforce troops on the western bank of the Dnipro River, which splits Kherson city.
On Tuesday, the UK stopped short of saying there was a breakthrough.
"It is not yet possible to confirm the extent of Ukrainian advances," the ministry said.
"Most of the units around Kherson are likely under-manned and are reliant upon fragile supply lines by ferry and pontoon bridges across the Dnipro".
Ed Arnold, a research fellow at the Royal United Services Institute, a British defence and security think tank, said the push represented the decisive phase of Ukraine's counteroffensive.
“We have been expecting this for a number of months,” he said. “Shaping or preparatory activity has been ongoing for around two months, where Ukraine has targeted Russian positions, ammunitions supplies to try to degrade their artillery strength and also bridges over the Dnipro River, which is just to the east of Kherson city.
“So, now what we expect to see is a Ukrainian counteroffensive to take at least the city of Kherson and potentially more territory to the east of the river.”
Mr Arnold said the city as important because it was one of the first places taken by Russian forces at the start of the conflict in February.
“[It is] also politically significant because the Ukrainian government and President Zelenskyy has to show the West he is able to use all of these western-supplied weapons systems to actually take back territory. So that is really important.
“And at the moment, once Kherson, at least the city, is in Ukrainian control that means there are no Russian forces to the north or west of the Dnipro River, which essentially dissects the whole of Ukraine,” Mr Arnold said.
“It protects Mykolaiv and Odesa further down the coast. It puts a lot of pressure on Russian forces in the south and particularly Crimea.”
Kremlin spokesman Dmitry Peskov said there was no reason to believe that the Kremlin's operations in southern Ukraine had suffered a set back. "The special military operation continues, it continues methodically, and in co-ordination with the current plans," he said. "All objectives will be fulfilled."
Ukraine’s southern offensive comes after weeks of stalemate in a conflict that has killed thousands and displaced millions, destroying cities and disrupting global energy prices and grain supplies.
Fears have also been raised of an impending radiation disaster at Europe's biggest nuclear power station after weeks of shelling near the Zaporizhzhia plant, which has been occupied by Russian troops since the early stages of the war.
UN nuclear inspectors said they were on their way to Ukraine on Monday, in a mission to stop the conflict from causing a disaster.
The International Atomic Energy Agency (IAEA) team will later this week inspect the plant and assess any damage.
Led by IAEA chief Rafael Grossi, the mission will evaluate working conditions and check safety and security systems, the Vienna-based organisation said.
It will also “perform urgent safeguards activities”, a reference to keeping track of nuclear material.
The UN, US and Ukraine have called for the withdrawal of military equipment and personnel from the complex to ensure it is not a target.
The Kremlin has ruled out abandoning the site.
In Kherson, Ukraine's Suspilne public broadcaster reported explosions in the area on Tuesday and city residents reported in social media posts hearing gunfire and explosions, but said it was not clear who was firing.
Ukraine's military general staff, in an early Tuesday update, reported clashes in various parts of the country but gave no information on the Kherson offensive.
In Moscow, the Defence Ministry said the offensive had “failed” after Ukrainian troops sustained “significant casualties”.
The “enemy's offensive attempt failed miserably”, RIA news agency reported.
A Ukrainian barrage of rockets left the Russian-occupied town of Nova Kakhovka without water or power, officials at the Russian-appointed authority told RIA news agency.
News agency Reuters said it could not verify the battlefield reports.
Russian shelling of the port city of Mykolaiv, which has remained in Ukrainian hands despite repeated Russian bombardments, killed at least two people, wounded about 24 and wiped out homes, city officials and witnesses said on Monday.
A Reuters correspondent reported a strike hit a family home directly next to a school, killing one woman.
The owner of the property, Olexandr Shulga, said he had lived there his entire life and that his wife was killed when she was buried by debris.
“It hit and the shock wave came. It destroyed everything,” he said.
Russia invaded Ukraine on February 24 in what it calls a “special military operation” to rid its neighbour of nationalists and protect Russian-speaking communities in the east of the country.
Ukraine and its allies describe it as an unprovoked war of aggression.
The conflict, the biggest attack on a European state since 1945, has largely settled into a war of attrition, mainly in the south and east, marked by artillery bombardments and air strikes. Russia captured swathes of the south early on.