Heavy fighting was underway Sunday in the northern parts of the frontline hotspot Bakhmut, while Russian missile strikes on Ukraine's second-largest city Kharkiv wounded five people.
Despite the flow of Western weapons to Ukraine, Russia has in recent days claimed gains around war-ravaged Bakhmut in the eastern region of Donetsk.
However, the head of Russia's mercenary group Wagner said Sunday that the Ukrainian army was not retreating and that fighting raged on in northern parts of Bakhmut.
"In the northern quarters of Artemovsk, fierce battles are going on for every street, every house, every stairwell," Yevgeny Prigozhin said in a statement, referring to Bakhmut by its old name.
"The Ukrainian armed forces are fighting to the last," he said.
Russian forces have been trying to seize control of Bakhmut in the eastern region of Donetsk for months in what has become the longest and bloodiest battle since Russia invaded Ukraine last February.
- 'I came to pray for peace' -
The fight for Bakhmut has turned the town with a pre-war population of roughly 75,000 into a ghost town dotted with hedgehog anti-tank defences and burnt-out cars. The town has no water, gas or electricity.
About 20 people, including two soldiers, attended a Sunday mass in the basement of the golden-domed All Saints' church in the deserted town.
Three women sang hymns, punctuated by sounds of mortar shells in the background.
The room was lit by two dozen candles and a portable light used by the two priests to read from the sacred book.
"Today I prayed that everything will be better for me after I die," said 20-year-old Serafim Chernyshov standing outside the church, with loud sounds of a steady exchange of small arms fire and the pounding of mortar shells to and from Russian positions echoing in the background.
"Last night, a missile flew into my garden and a bullet flew inside my house, it could have hit me," he added. "I might die now or in 30 years. If I'm killed, it will be God's will."
"I came to pray for peace," added Lyubov Avramenko, 84.
Ukrainian President Volodymyr Zelensky said on Friday that Kyiv's troops would fight for Bakhmut "as long as we can."
He urged the West to supply Kyiv with sophisticated weapons to help his forces retain control of Bakhmut and speed up deliveries of heavy tanks.
In his evening address on Saturday, Zelensky acknowledged that the situation was getting tougher.
Russia, he said, was "throwing more and more of its forces at breaking down our defence".
"It is very difficult now in Bakhmut, Vugledar, Lyman and other areas," he added, referring to the frontline towns in the east of the country.
The British defence ministry said on Sunday that over the past week, Russia had made "small advances" in its attempt to encircle Bakhmut.
The two main roads into the city for Ukrainian troops "are likely now both threatened by direct fire, following the Russian advances," the British defence ministry said.
"Bakhmut is increasingly isolated."
- Missile strikes in Kharkiv -
For months Moscow has systematically targeted Ukraine's civilian infrastructure, including the energy grid, leaving millions in the dark and cold in the middle of winter.
In Ukraine's second city Kharkiv, a missile strike hit a residential building on Sunday, wounding four people, said Oleg Synegubov, head of the regional administration. Another strike left a security guard injured when a missile hit an institute in the northeastern city, he said.
On Saturday, "the Russians killed four residents of the region of Donetsk," said Pavlo Kyrylenko, head of the regional administration, adding that another 11 people were injured.
- Oil and corruption -
On Sunday, Russia faced a fresh turn of the sanctions screw, with an embargo on ship deliveries of its refined oil products.
The European Union, the Group of Seven industrialised nations and Australia will cap the price of Moscow's refined oil products.
In December, the EU already imposed an embargo on Russian crude oil coming into the bloc by sea and -- with its G7 partners -- imposed a $60-per-barrel cap on Russian crude exports to other parts of the world.
The new embargo and price caps starting Sunday will target Russian refined oil products such as petrol, diesel and heating fuel arriving on ships.
The Kremlin has warned that the measures will destabilise world markets.
In Kyiv, Ukrainian Defence Minister Oleksiy Reznikov was set to hold a news conference as authorities press ahead with a drive to stamp out corruption under pressure from Western donors, after graft scandals linked to the war effort.