In its Monday evening update, Ukraine's army General Staff said Russian artillery pounded about 25 towns and villages around Bakhmut and Avdiika, the two focal points of Russian attempts to advance in the strategic eastern industrial Donbas region.
It said Russia also kept up shelling more than 30 settlements in the northeast Kharkiv and Sumy areas near the Russian border.
In the south, Russian mortar and artillery fire hit several towns, including the regional capital Kherson, which Russian forces abandoned in November.
Reuters was not able to verify battlefield reports.
The death toll from Saturday's missile strike in Dnipro rose to 40, including three children, Ukrainian officials said.
They said 25 people were missing or unaccounted for but 39 people, including six children, were rescued from the rubble.
"What happened in Dnipro, the fact that Russia is preparing new attempts to seize the initiative in the war, the fact that the nature of military action at the front requires new decisions on arms supplies - only underscores how important it is to co-ordinate all the efforts of the coalition defending Ukraine and freedom," President Volodymyr Zelenskiy said in his Monday night video address.
"And to speed up decision-making."
Western countries have produced a steady supply of weapons to Ukraine since Russian forces invaded on February 24 but Zelenskiy and his government insist they need tanks.
Britain confirmed on Monday it would send 14 Challenger 2 tanks and other hardware including hundreds more armoured vehicles and advanced air defence missiles.
United States Defense Secretary Lloyd Austin is due to host allies at an air base in Germany on Friday to discuss further aid for Ukraine.
Moscow denies deliberately targeting civilians, although the war has displaced millions, killed thousands of civilians and left Ukrainian cities, towns and villages in ruins.
Russia calls its actions a "special military operation" to protect its security because its neighbour grew increasingly close to the West.
Ukraine and its allies accuse Moscow of an unprovoked war to grab territory and erase the independence of a fellow ex-Soviet republic.
Moscow claimed last week to have captured the eastern Ukrainian salt mining town of Soledar, in what would be its biggest battlefield success since August.
Ukraine says it still has some presence in the town and fighting continues.
"We are always amazed by the stubborn nature of the Ukrainian regime which says some sort of fighting is still going on in Soledar," Denis Pushilin, head of the Donetsk People's Republic now annexed by Russia, said in a video on the Telegram messaging app.
"There is absolutely nothing of the sort."
He said units of the mercenary Wagner Group "are conducting mopping up operations".
The group was founded by Yevgeny Prigozhin, an ally of Russian President Vladimir Putin.
Pushilin also said there were civilian casualties when Ukrainian forces shelled shops in Donetsk, a city that has been under the control of Russian separatists since 2014.
Reuters was unable to verify the reports on Soledar and Donetsk.
Oleskiy Danylov, Secretary of Ukraine's Security Council, also mentioned on Monday night the need for an acceleration in weapons supplies because the government expected Russia "to attempt to make a so-called final push".
Danylov told Ukrainian television that could take place on the invasion's anniversary or in March.
"We must prepare for such events every day. And we are preparing ... The first and last question is always about weapons, aid to help us defeat this aggressor that invaded our country," Danylov said.
