Meanwhile, Britain has became the first Western country to offer it the heavy tanks it has long been seeking.
The British move drew a swift reaction from Moscow which warned it would only “intensify” the conflict.
In other developments, Moldova said debris from the latest Russian missiles had landed on its territory and condemned the attacks.
Ukraine also insisted Saturday that the fighting in Soledar was continuing, a day after Russia’s claim that it had captured the ravaged eastern town following a long battle.
Victory there would be a rare achievement for Moscow after a series of military setbacks.
Mykhaylo Podolyak called for Russia to be expelled from the UN Security Council.
UK sending first heavy tanks
Earlier Saturday, British Prime Minister Rishi Sunak pledged to provide Challenger 2 tanks to Ukraine, the first Western country to supply the heavy tanks Kyiv has been crying out for.
Russia’s embassy in the UK swiftly issued a warning that “bringing tanks to the conflict zone, far from drawing the hostilities to a close, will only serve to intensify combat operations, generating more casualties, including among the civilian population”.
But in his evening address on Saturday, Zelensky argued that Russian “terror” could only be stopped on the battlefield.
“This can and must be done on our land, in our sky, in our sea,” he said. Moldova, Ukraine’s southwestern neighbour, said Saturday it had found missile debris on its territory after the latest Russian strikes.
“Russia’s brutal war against Ukraine directly impacts Moldova again,” President Maia Sandu tweeted, posting photos of the wreckage.
Ukraine’s energy facilities operator Ukrenergo said it was working on “eliminating the consequences” of the latest Russian strikes.
In Kyiv, AFP journalists heard several explosions, while Ukrainian officials reported strikes on a power facility.
“There is a hit to an infrastructure facility, without critical destruction or fire,” the Kyiv city administration said.
In the northeastern Kharkiv region, “the enemy launched another missile attack on critical infrastructure and industrial facilities,” governor Oleg Synegubov said.
Emergency blackouts were applied in “most regions” of Ukraine due to the fresh barrage of attacks, energy minister German Galushchenko said Saturday.
Attacks were also reported in the southern Zaporizhzhia region. Zelensky said Ukraine had managed to shoot down 20 of the more than 30 Russian missiles fired.
“Unfortunately, energy infrastructure facilities have been also hit,” he added, with the Kharkiv and Kyiv regions suffering the most.
Soledar’s status disputed
There was still uncertainty about the fate of Soledar, a salt mining outpost that Russia claimed to have captured, against denials from Ukraine.
Both sides have conceded heavy losses in the battle for the town. Ukraine’s military governor in the embattled eastern region of Donetsk insisted Saturday that “Soledar is controlled by Ukrainian authorities, our military controls it.” The “battles continue in and outside of the city”, he added. He was responding to claims by Russia’s defence ministry on Friday that it had “completed the liberation” of Soledar the previous day.
The industrial town with a pre-war population of about 10,000 has now been reduced to rubble through intense fighting.
Capturing Soledar could improve the position of Russian forces as they push towards what has been their main target since October -- the nearby transport crossroads of Bakhmut.
Turkey said Saturday it was ready to push for local ceasefires in Ukraine and warned that neither Moscow nor Kyiv had the military means to “win the war”.
President Recep Tayyip Erdogan’s foreign policy adviser Ibrahim Kalin conceded that it seemed unlikely that the warring sides were ready to strike an “overarching peace deal” in the coming months.