Ukrainian troops are still holding the strategic eastern town of Bakhmut, despite repeated Russian attacks, while the situation in the Donbas region remains very difficult, President Volodymyr Zelensky has said.
Mr Zelensky, speaking in an evening address, also said Russian missiles and drones had continued to hit Ukrainian cities, causing destruction and casualties.
Although Ukrainian troops have recaptured thousands of square kilometres of land in recent offensives in the east and south, officials say progress is likely to slow once Kyiv's forces meet more determined resistance.
Fighting is particularly intense in the eastern Donetsk and Luhansk provinces bordering Russia. Together they make up the larger industrial Donbas, which Moscow has yet to fully capture.
Russian forces have repeatedly tried to seize Bakhmut, which sits on a main road leading to the cities of Sloviansk and Kramatorsk. Both are situated in the Donetsk region.
"Active fighting continues in various areas of the front. A very difficult situation persists in the Donetsk region and Luhansk region," Mr Zelensky said.
"The most difficult (situation) is in the direction of Bakhmut, as in previous days. We are holding our positions."
Separately, the Ukrainian armed forces' general staff said in a Facebook post that troops had on Saturday repelled a total of 11 separate Russian attacks near Kramatorsk, Bakhmut and the town of Avdiivka, just to the north of Donetsk.
Meanwhile, the Russian-state news agency RIA has said that at least 11 people have been killed and 15 more wounded at a training ground in southwestern Russia, when two attackers opened fire on a group of volunteers who wished to fight in Ukraine.
RIA, citing the defence ministry, said the two assailants had been shot dead after the attack in the Belgorod region, which borders Ukraine. It said they were nationals from a former Soviet republic, but did not give any details.
Earlier, Russian President Vladimir Putin said Moscow was "doing everything right" in its nearly eight-month invasion of Ukraine despite a string of embarrassing defeats against Kyiv's forces, who will receive $725 million in new US military assistance.
Mr Putin's comments yesterday came hours after Kremlin-installed officials in the southern Kherson region urged residents to leave as Kyiv said its soldiers were advancing on the oblast's main city.
Moscow also hinted at the extent of the damage dealt to the Crimea bridge - the sole land connection between its mainland and the annexed Ukrainian peninsula - following a blast last Saturday, saying it could take many months to complete repairs.
"What is happening today is not pleasant. But all the same, (if Russia had not attacked in February) we would have been in the same situation, only the conditions would have been worse for us," Mr Putin told reporters after a summit in the capital of Kazakhstan.
"So we're doing everything right," he insisted.
He did, however, acknowledge that Russia's ex-Soviet allies were "worried".
Mr Putin said there was no need for further massive strikes against Ukraine at present and claimed the Kremlin did not intend to destroy its pro-Western neighbour.
"There is no need now for massive strikes. There are other tasks. For now," he said.
He spoke days after Russia unleashed a wave of missile strikes on cities across Ukraine that left at least 20 civilians dead.
Mr Putin said the strikes were in retaliation for the explosion on the Crimea bridge, which he has described as a "terrorist act".
The bridge is a logistically crucial transport link for moving military equipment to Russian soldiers fighting in Ukraine.
Washington announced yesterday an additional $725 million in military assistance to Kyiv, including more ammunition for the Himars rocket systems that have been used by Ukraine to wreak havoc on Russian targets.
The aid comes "in the wake of Russia's brutal missile attacks on civilians across Ukraine" and "mounting evidence of atrocities by Russia's forces," US Secretary of State Antony Blinken said in a statement.
It brings the total US military assistance to Ukraine to $17.6 billion since the Russian invasion on February 24.
"We will continue to stand with the people of Ukraine as they defend their freedom and independence with extraordinary courage and boundless determination," Blinken said.
Separately, Elon Musk said his SpaceX would not be able to pay indefinitely for the Starlink satellite internet vital to Ukraine's communications in the fight against Russian invaders.
The US military confirmed it was communicating with the billionaire's company about funding for the key network.
Ukraine, which is clawing back territory in both the east and south, feted its first Defenders Day public holiday since the start of Moscow's invasion, pledging victory.
Meanwhile, in southern Ukraine, Kyiv's forces have been pushing closer and closer to Kherson, the main city in the region of the same name just north of Crimea.
Yesterday, Moscow-installed authorities renewed a call for residents to temporarily leave.
"The bombardment of the Kherson region is dangerous for civilians," Kirill Stremousov, deputy head of the pro-Russian regional administration said, and urged residents to take a trip for "rest and recreation" elsewhere.
Kyiv, which announced its counter-offensive in the south in August, said it has already recaptured more than 400 square kilometres (155 miles) in the Kherson region in under a week.
But in the east, pro-Russian forces said they were closing in on the industrial city of Bakhmut after reporting the capture of two villages on the city's outskirts this week.
An official of the so-called Lugansk People's Republic, a pro-Kremlin breakaway region in east Ukraine, said "active hostilities were under way" within Bakhmut.
"Our forces are confidently marching and liberating this settlement," the official, Andriy Marochko, was quoted as saying by Russia's state-run TASS news agency.
