Avdiivka, another major Russian target, the nearby town of Maryinka and some neighbouring settlements were also hit, the military added.
In Kramatorsk, about 55 km (34 miles) northwest of Bakhmut, a Russian missile destroyed one apartment building and damaged seven on Wednesday, killing at least three people and injuring 20, police said.
"Definite increase has been noted in the offensive operations of the occupiers on the front in the east of our country. The situation has become tougher," Zelenskiy said.
"The enemy is trying to achieve at least something now to show that Russia has some chances on the anniversary of the invasion," he added in an evening video address.
Zelenskiy vowed more anti-corruption measures as authorities continued raids ahead of a meeting in Kyiv with more than a dozen top European Union officials on Friday, reflecting a determination to show that Ukraine can be a reliable steward of billions of dollars in aid.
Ukraine sees the meeting as important to its hopes of joining the bloc, which can take years.
Earlier, security officials searched the home of businessman Ihor Kolomoiskiy, a one-time Zelenskiy ally, in what media said was an investigation of suspected financial crime.
Kolomoiskiy could not immediately be reached for comment. He has denied any wrongdoing.
MISSILE HITS KRAMATORSK
In Kramatorsk, police said a Russian Iskander-K tactical missile struck at 9:45 p.m. (1945 GMT).
"At least eight apartment buildings were damaged. One of them was completely destroyed," police said in a Facebook post.
"People may remain under the rubble."
At least 44 people were killed in January when a Russian missile hit an apartment building in Dnipro city.
In April 2022, Ukraine said 57 people died when a Russian missile hit the train station in Kramatorsk. Russia, which denies targeting civilians, said the missile was Ukrainian.
A former commander of Russia's Wagner mercenary group who fled to Norway in January told Reuters he wanted to apologise for fighting in Ukraine and was speaking out to bring perpetrators of atrocities to justice.
"First of all, repeatedly, and again, I would like to apologise," Andrei Medvedev, 26, said.
Ukraine and its Western allies have accused Russian forces of war crimes. Russia rejects that.
The Wagner group has been locked in a battle of attrition in Donetsk.
'WE NEED WEAPONS'
Donetsk and Luhansk, declared annexed by Russia in September following sham referendums, make up Ukraine's industrial region of Donbas - the target of Russian forces after a failed advance on the capital, Kyiv, early in the campaign.
In the past 24 hours, Ukrainian forces repelled attacks on several centres in Donetsk, including Bakhmut, Krasna Hora, and Blahodatne, Ukrainian military analyst Oleh Zhdanov said.
Russian forces said they took Blahodatne, just to the north of Bakhmut, on Tuesday.
They were also pushing to the south of Bakhmut, using their superior troop numbers to try to cut it off from re-supply and force the Ukrainians out, Ukrainian military analyst Yevhen Dikiy said.
"This for us is the most difficult scenario," Dikiy told Espreso TV, referring to what he called a "measure of success" for Russian forces.
"The enemy is able to use its sole resource, which it has in excess, its men."
Reuters could not confirm battlefield reports.
Russia and Ukraine are both believed to be preparing new offensives and Ukrainian Defence Minister Oleksii Reznikov said a Russian push could begin around the symbolically important date of Feb. 24.
"We keep telling our partners that we have to be ready for this, as quickly as possible. And that's why we need weapons," Reznikov, visiting Paris on Tuesday, told France's BFM TV.
Ukraine has secured pledges of weapons from the West offering new capabilities - the latest expected this week to include rockets from the United States that would nearly double the range of Ukrainian forces.
The Kremlin said that longer-range rockets from the United States would escalate the conflict but not change its course.
President Vladimir Putin sent troops into Ukraine last year for a "special military operation" to "demilitarise" and "denazify" its neighbour but he now casts the campaign as a fight to defend Russia against an aggressive West.
Ukraine and the West accuse Russia of waging an illegal war to expand its territory.