Ukrainian servicemen walk in a trench at a position near a frontline in Donetsk Region, Ukraine. Reuters
"Our heroes do not give up positions in Severodonetsk. In the city, fierce street fighting continues," Zelensky said in his nightly video address on Monday.
"And the Ukrainian Donbas stands, stands strong," he added referring to the region where Severodonetsk is located.
It was unclear which side had the upper hand, with "the situation changing from hour to hour", Oleksandr Stryuk, head of administration in Sievierodonetsk, said on television.
Russia denies targeting civilians in the conflict.
The city has become the main target of the Russian offensive in the Donbas — comprising Luhansk and Donetsk provinces — as the Kremlin's invasion grinds on in a war of attrition that has seen cities laid waste by artillery barrages.
Ukraine's defence ministry said Russia was also throwing troops and equipment into its drive to capture the largest remaining Ukrainian-held city in Luhansk.
Luhansk Governor Serhiy Gaidai said earlier on Monday the situation had worsened after Ukrainian defenders had pushed back the Russians over the weekend as they seemed close to victory.
In its nightly update, the Ukrainian military said two civilians were killed in Russian shelling in the Donetsk and Luhansk regions on Monday and that Russian forces had fired at more than 20 communities.
A view shows a residential building destroyed by a Russian military strike in Bakhmut, Donetsk. Reuters
Reuters could not independently verify the battlefield reports. Russia denies targeting civilians in the conflict.
Russia says it is on a mission to "liberate" the Donbas — partly held by separatist proxies of Moscow since 2014 — after Ukrainian forces pushed its troops back from the capital Kyiv and Ukraine's second city Kharkiv in the war's early stages.
Russia invaded Ukraine on Feb. 24, but calls its action a "special military operation" to stamp out what it sees as threats to its security. Ukraine and its Western allies call this a baseless pretext for a war to grab territory that risks turning into a wider European conflict.
An official with the Russia-backed Donetsk People's Republic said Pisky, on the frontlines just 10 km (6 miles) northwest of provincial capital Donetsk, was under control of Russian and separatist forces.
Kyiv said on Friday it had launched new air strikes in the captured southern region of Kherson, one of the first areas to be taken by Russia after the February 24 invasion.
Governor Dmytro Zhyvytskyy posted photographs of the charred shell of a four-story building and rescuers searching rubble. In a later Facebook post, he said many Russian soldiers and some local residents also were killed during the fighting on Sunday.
Kathy Lueders, who heads the agency's human spaceflight program, told reporters on a call that operations on the research platform were proceeding "nominally" and "we're not getting any indications at a working level that our counterparts are not committed."
Macron on Wednesday criticized the legislation, known as the Inflation Reduction Act, during a luncheon with US lawmakers and again during a speech at the French embassy.
The awards were held to coincide with the 20th MEADFA conference which was held in Bahrain for the first time and brought together 440 delegates.
Weeks before the invasion, Xi and Russian leader Vladimir Putin affirmed their "no limits" relationship, and Beijing has stepped up oil purchases from Russia while their air forces held joint drills this week.