The head of Russia's private Wagner militia said on Sunday that fierce fighting was ongoing in the northern parts of the Ukrainian city of Bakhmut, which has been the focus of Russian forces' attention for weeks. Yevgeniy Prigozhin, the founder and head of the Wagner group, said his soldiers were "fighting for every street, every house, every stairwell" against Ukrainian forces who were not retreating. Russian forces have been attempting to encircle and capture Bakhmut, a city in the eastern Donbas region, for weeks, and appear to be making slow, grinding and costly progress. Ukrainian President Volodymyr Zelenskiy has said repeatedly in recent days that the situation around the city is tough. "Nobody will give away Bakhmut. We will fight for as long as we can. We consider Bakhmut our fortress," he said on Friday. Britain's defense ministry said on Sunday Russia had made "small advances" in its attempt to encircle Bakhmut. If Russian forces manage to capture the city, which has been decimated by months of artillery shelling, it would be their most important strategic advance since last summer, when an initial offensive through the east of Ukraine came to a halt and was eventually reversed in a series of stunning Ukrainian counter offensives in the second half of 2022. Prigozhin rejected reports in Russian media outlets that Ukrainian troops were abandoning Bakhmut. "Ukrainian forces are not retreating anywhere. They are fighting to the last," he said in a statement published on his Telegram channel. "Fierce battles are going on in the northern quarters for every street, every house, every stairwell," he added.