Ukraine's general staff said the Russians were pulling back from the northeastern city of Kharkiv and focusing on guarding supply routes while launching mortar, artillery and airstrikes in the eastern Donetsk province in order to ``deplete Ukrainian forces and destroy fortifications.''
Defense Minister Oleksii Reznikov said Ukraine was ``entering a new - long-term - phase of the war.''
President Volodymyr Zelenskyy said Ukrainians were doing their ``maximum'' to drive out the invaders and that the outcome of the war would depend on support from Europe and other allies.
``No one today can predict how long this war will last,'' Zelenskyy said in his nightly video address late Friday.
After Russian forces failed to capture Kyiv following the Feb. 24 invasion, President Vladimir Putin shifted his focus eastward to the Donbas, an industrial region where Ukrainian troops have battled Moscow-backed separatists since 2014.
Russia's offensive aims to encircle Ukraine's most experienced and best-equipped troops, who are based in the east, and to seize parts of the Donbas that remain in Ukraine's control.
Getting a full picture of the direction the fighting in the east is taking has been difficult because airstrikes and artillery barrages have made it extremely dangerous for reporters to move around. But the battle appears to be a back-and-forth slog with no major breakthroughs on either side.
Russia has captured some Donbas villages and towns, including Rubizhne, a city with a prewar population of around 55,000.
Zelenskyy said Ukraine's forces had also made progress in the east, retaking six Ukrainian towns or villages in the past day.
Kharkiv, which is not far from the Russian border and only 80 kilometres (50 miles) southwest of the Russian city of Belgorod, has undergone weeks of intense shelling. The largely Russian-speaking city with a prewar population of 1.4 million was a key Russian military objective earlier in the war when Moscow hoped to capture and hold major Ukrainian cities.
Ukraine ``appears to have won the Battle of Kharkiv.'' the Institute for the Study of War, a Washington-based think tank, said. ``Ukrainian forces prevented Russian troops from encircling, let alone seizing Kharkiv, and then expelled them from around the city, as they did to Russian forces attempting to seize Kyiv.''
Regional governor Oleh Sinegubov said in a post on the Telegram messaging app that there had been no shelling attacks on Kharkiv in the past day.
He said Ukraine had launched a counteroffensive near Izyum, a city 125 kilometres (78 miles) south of Kharkiv that has been under effective Russian control since at least the beginning of April.
Fighting was fierce on the Siversky Donets River near the city of Severodonetsk, where Ukraine has launched counterattacks but failed to halt Russia's advance, said Oleh Zhdanov, an independent Ukrainian military analyst.
``The fate of a large portion of the Ukrainian army is being decided, there are about 40,000 Ukrainian soldiers,'' he said.
However, Russian forces suffered heavy losses in a Ukrainian attack that destroyed a pontoon bridge they were using to try to cross the same river, the largest in eastern Ukraine, in the town of Bilohorivka, Ukrainian and British officials said, in another sign of Moscow's struggle to salvage a war gone awry.
Britain's Defense Ministry said Russia lost ``significant armoured manoeuvre elements`` of at least one battalion tactical group in the attack. A Russian battalion tactical group consists of about 1,000 troops.
The ministry said the risky river crossing was a sign of ``the pressure the Russian commanders are under to make progress in their operations in eastern Ukraine.''
Zelenskyy said in his nightly video address to the nation that Ukrainians were doing everything they could to drive out the Russians, but ``no one today can predict how long this war will last.''
``This will depend, unfortunately, not only on our people, who are already giving their maximum,'' he said. ``This will depend on our partners, on European countries, on the entire free world.''
The Ukrainian leader warned that the war causing a food crisis around the world as a Russian blockade stops Ukrainian grain from leaving port.
The Group of Seven leading economies echoed that warning, saying Saturday that ``Russia's war of aggression has generated one of the most severe food and energy crises in recent history, which now threatens those most vulnerable across the globe.''
Putin launched the war in Ukraine aiming to thwart NATO's expansion in Eastern Europe. But the invasion of Ukraine has other countries along Russia's flank worried they could be next.
This week, the president and prime minister of Finland said they favoured their country seeking NATO membership. Officials in Sweden are expected to announce a decision Sunday on whether to apply to join the Western military alliance.
Putin told Finnish President Sauli Niinisto that there are no threats to Finland's security and that joining NATO would be an ``error'' that would ``negatively affect Russian-Finnish relations.''
The Kremlin said the two leaders had a ``frank exchange of views'' in a phone call on Saturday.
Niinisto said the discussion ``was straightforward and unambiguous and was held without exaggeration. Avoiding tensions were considered important.''
Russia's response to the moves by Finland and Sweden has so far been muted, though Deputy Foreign Minister Alexander Grushko said Saturday that their accession to NATO would heighten security tensions in the Arctic, ``turning it into an arena of military competition.''
The Nordic nations' potential bids were thrown into question Friday when Turkish President Recep Tayyip Erdogan said his country is ``not of a favourable opinion'' toward the idea.