Moscow says taking Pokrovsk, dubbed "the gateway to Donetsk" by Russian media, would give it a platform to drive north towards the two biggest remaining Ukrainian-controlled cities in the Donetsk region - Kramatorsk and Sloviansk.
Russia has been threatening Pokrovsk for more than a year, using a pincer movement to attempt to encircle it and threaten supply lines, rather than the deadly frontal assaults it employed to capture the city of Bakhmut in 2023.
Ukrainian President Volodymyr Zelenskiy described the situation around Pokrovsk as difficult and his top commander, Oleksandr Syrskyi, acknowledged his army's position in parts of southeastern Zaporizhzhia region had "significantly worsened".
Russian war bloggers published a video on Tuesday showing what they said were Russian forces entering Pokrovsk along a road enveloped in fog, in what some Telegram users said looked like scenes from the 1979 action film Mad Max, which unfolds in a post-apocalyptic landscape.
The video showed Russian forces on motorcycles and in an odd assortment of cars and other vehicles. Many vehicles, missing doors and windows, were shown driving along a road strewn with debris as soldiers looked on. Some Russian soldiers sat on the roof of a battered vehicle. A drone was seen beside the road.
Reuters was able to confirm the location of the video as Pokrovsk from the road layout, signs, utility tower, and trees seen in the video, which matched file and satellite imagery of the area. Reuters was not able to independently verify the date of the footage.
In a Telegram post, Zelenskiy, who was visiting Ukrainian-held parts of southern Kherson region, described the situation in Pokrovsk as "difficult, particularly as weather conditions favour attacks. But we are continuing to destroy the occupiers."
Zelenskiy also said Moscow was increasing its assaults in the southeastern region of Zaporizhzhia.
Top commander Syrskyi said Russian forces were exploiting foggy conditions to infiltrate positions in Zaporizhzhia.
"The situation has significantly worsened in the Oleksandrivka and Huliaipole directions, where, using its numerical superiority in personnel and materiel, the enemy advanced in fierce fighting and captured three settlements," Syrskyi wrote on Telegram.
Ukrainian troops, he wrote, were fighting "exhausting battles" for two villages northeast of Huliaipole.
Ukraine's military said about 300 Russian soldiers were now inside Pokrovsk and that Moscow had intensified efforts to get more troops in over the past few days. It said Ukrainian forces were battling Russian groups in the city.
Syrskyi told the New York Post that Russia was concentrating some 150,000 troops in a drive on Pokrovsk.
In a sign of the intensity of the urban battle, Russia said it had taken 256 buildings. Its forces were advancing to the northwest and east of Pokrovsk and around the railway station.
Moscow and Kyiv have given different accounts of the battle for Pokrovsk: Moscow has for days said the city is encircled while Kyiv has denied Moscow controls it and said that it was still able to supply neighbouring Myrnohrad.
Open source battlefield maps from both sides show that Russia has executed a pincer movement around the city and was close to closing it, though Kyiv has counter-attacked around the town of Dobropillia.
Russia's military says it now controls more than 19 per cent of Ukraine, or some 116,000 sq km. Ukrainian maps tracking frontline changes show Russian control at 19.1 per cent of Ukraine, up from 18 per cent nearly three years ago.
