A Ukrainian counteroffensive was underway near the Russian-held town of Izium, but its military reported on Sunday that Russian forces were advancing elsewhere in the Donbas region, which has become the main theatre of war over the past month.
Having resisted fiercely since Russia launched its invasion on Feb. 24, Ukraine's military has notched a string of successes, first forcing Russia's commanders to abandon an advance on the capital Kyiv, and then making rapid gains in the northeast in recent week to drive the enemy away from the second biggest city of Kharkiv.
Since mid-April, Russian forces have focussed much of their firepower on the east for what has become known as the "Battle of the Donbas".
Delivering an update on Sunday morning, Ukraine's military said: "Despite losses, Russian forces continue to advance in the Lyman, Sievierodonetsk, Avdiivka and Kurakhiv areas in the broader Donbas region."
Ukraine's military reported destroying eight Russian tanks, five artillery systems, along with other armoured vehicles, and drones in fighting across the Donbas over the previous day.
A regional governor said Ukrainian forces had mounted a counter attack near Izium, a strategic city straddling the Donets river, about 120 km (75 miles) southeast on the highway from Kharkiv.
"The hottest spot remains the Izium direction," Governor Oleh Sinegubov said in comments aired on social media. "Our armed forces have switched to a counteroffensive there. The enemy is retreating on some fronts and this is the result of the character of our armed forces."
Reuters could not independently verify the Ukrainian reports.
But British military intelligence delivered a damning assessment on Sunday of Russia's Donbas campaign. It reckoned that Russia had lost about a third of the ground combat force deployed in February, and its offensive in the Donbas had fallen "significantly behind schedule" and was unlikely to make rapid advances during the coming 30 days.
Keeping up pressure on Izium and Russian supply lines will make it harder for Moscow to encircle battle-hardened Ukrainian troops on the eastern front in the Donbas.
Russia's defence ministry said its forces killed at least 100 Ukrainian "nationalists" in a series of strikes on military sites, including in the Donbas. Reuters could not independently verify that report.
Ukrainian President Volodymyr Zelenskiy said the situation in Donbas remained very difficult, adding that Russian forces were still trying to salvage some kind of victory there.
"They are not stopping their efforts," he said.
Elsewhere, the Ukrainian military said there was no let-up on Sunday in Russia's bombardment of the steel works in the southern port of Mariupol, where a few hundred Ukrainian fighters are holding out weeks after the city fell into Russian hands.
Zelenskiy said talks were underway seeking a way to evacuate wounded soldiers from Mariupol in return for the release of Russian prisoners of war.
A large convoy of cars and vans carrying refugees from the ruins of Mariupol arrived in the Ukrainian-controlled city of Zaporizhzhia after nightfall on Saturday after waiting days for Russian troops to allow them to leave.
Russia, rejecting Ukraine's claim to have struck and set alight a modern navy logistics ship in the Black Sea, showed photos of what it said was the Vsevolod Bobrov with no signs of damage.
On Saturday night, Ukraine celebrated a morale-boosting triumph in the Eurovision Song Contest that was seen as sign of the strength of popular support for Ukraine across Europe.
"Our courage impresses the world, our music conquers Europe! Next year Ukraine will host the Eurovision song contest," Zelenskiy said in an online message after Kalush Orchestra won with their entry "Stefania".
Eurovision's winners traditionally get to host the event the following year.
In another token of international solidarity, U.S. Republican senators paid an unannounced visit to Kyiv. The delegation discussed further strengthening sanctions on Russia, Zelenskiy said.
As well as losing large numbers of men and much military equipment, Russia has been hit by economic sanctions. The Group of Seven industrial powers pledged on Saturday to "further increase economic and political pressure on Russia" and supply more weapons to Ukraine.
Moscow's invasion, which it calls a "special operation" to disarm Ukraine and protect it from fascists, has jolted European security. Kyiv and its Western allies say the fascism assertion is a baseless pretext for an unprovoked war of aggression.
One of the aims of Russia's action in Ukraine was to prevent the former Soviet republic ever joining NATO.
But in a telephone call, Finnish President Sauli Niinisto told Russian President Vladimir Putin that his country, which shares a 1,300-km (800-mile) border with Russia, wanted to join the North Atlantic Treaty Organization to bolster its own security.
Putin told Niinisto it would be a mistake for Helsinki to abandon its neutrality, the Kremlin said, adding that the move could harm bilateral relations.
Turkey has not shut the door to Sweden and Finland joining NATO but wants negotiations with them and a clampdown on what it sees as terrorist activities, President Tayyip Erdogan's spokesman said, referring to the activities of Kurds living in the Nordic countries.