Five people were killed by shelling in the Ukrainian city of Mykolaiv on Friday and cluster munitions were used, Vitaliy Kim, the governor of Mykolaiv region, said on Telegram on Friday.
Russian shelling hit a residential area of Ukraine's eastern city of Kharkiv, killing seven people including a small child and wounding 34 others, the regional governor said on Friday.
Russia describes its invasion of Ukraine as a "special operation" and denies targeting civilian areas.
Ukraine said on Friday it was trying to break Russian forces' siege of Mariupol, with fighting raging around the city's Illich steelworks and port, as the capital Kyiv was rocked by some of the most powerful explosions in two weeks.
Mariupol, on the Sea of Azov, has seen the worst fighting of the war. Home to 400,000 people before Russia's invasion, the city has been reduced to rubble in seven weeks of siege and bombardment. Thousands of civilians have died and tens of thousands are still trapped in the city.
"The situation in Mariupol is difficult and hard. Fighting is happening right now. The Russian army is constantly calling on additional units to storm the city," defense ministry spokesperson Oleksandr Motuzyanyk said.
"But as of now the Russians haven't managed to completely capture it," he told a televised briefing.
Motuzyanyk said Russia had used long-range bombers to attack Mariupol for the first time since its Feb. 24 invasion, and that elsewhere Russian forces were concentrating efforts on seizing the cities of Rubizhne and Popasna in Ukraine's east.
Moscow has said its main war aim is to capture the Donbas, an eastern region of two provinces that are already partly held by the Russian-backed separatists, after its invasion force was driven from the outskirts of Kyiv earlier this month.
Ukrainian Deputy Prime Minister Iryna Vereshchuk said that 2,864 people had been evacuated from conflict areas on Friday, including 363 people from Mariupol who used their own transport.
Ukrainian President Volodymyr Zelensky recently made a direct appeal to US President Joe Biden for the United States to designate Russia a "state sponsor of terrorism," the Washington Post reported on Friday, citing people familiar with their conversation.
The list currently includes four countries: North Korea, Cuba, Iran and Syria.
A White House spokesperson declined to respond specifically to the report, adding, "We will continue to consider all options to increase the pressure on Putin."
RUSSIA'S MAIN TARGET
Mariupol is Russia's main target in the Donbas and Moscow has said it hopes to seize it soon, which would make it the only big city captured so far.
Russia's defense ministry said it had captured the Illich steel works. The report could not be confirmed. Ukrainian defenders are mainly believed to be holding out in Azovstal, another huge steel works.
Both plants are owned by Metinvest - the empire of Ukraine's richest businessman and backbone of Ukraine's industrial east - which told Reuters on Friday it would never let its enterprises operate under Russian occupation.
"We believe in the victory of Ukraine and plan to resume production after the end of hostilities," Metinvest told Reuters in a statement, adding its sites were damaged but that it was impossible to say by how much while fighting continued.
Ukraine's Deputy Prime Minister Iryna Vereshchuk said nine humanitarian corridors had been agreed for Friday to evacuate civilians, including by private car from the besieged city of Mariupol.
Other evacuation routes include ones from Berdiansk, Tokmak, Enerhodar and Sievierodonetsk.
Humanitarian corridors in Luhansk region will operate provided that the shelling by Russian forces ceases.
The governor of Ukraine's Luhansk region, Serhiy Gaidai, on Friday urged residents of six towns to evacuate, adding that one person had been killed and five wounded in Russian shelling of the town of Kreminna.
Gaidai wrote on the Telegram messaging app: "Don't hesitate and leave while that possibility remains. ... Choose life, buses are waiting for you at the pickup points. As are trains, of which there are enough."
Russia said it had struck overnight what it said was a factory in Kyiv that made and repaired anti-ship missiles, in apparent retaliation for the sinking of the Moskva, the flagship of Moscow's Black Sea fleet, on Thursday.
Ukraine said one of its missiles had caused the Moskva to sink, in a powerful symbol of its resistance to a better-armed foe. Moscow said the ship sank while being towed in stormy seas after a fire caused by an explosion of ammunition.
The United States believes the Moskva was hit by two Ukrainian missiles and that there were Russian casualties, although numbers were unclear, a senior US official said on Friday.
Russia has previously said more than 500 sailors on board the Moskva were evacuated after the blast. Neither that assertion nor the US assessment could be independently verified.
Motuzyanyk called Russia's loss of the Moskva significant. But he said he was not authorized to give information on the factory near Kyiv, which Moscow said its missiles had struck.
The Moskva was by far Russia's largest vessel in the Black Sea fleet, equipped with guided missiles to shoot down planes and attack the shore. It had radar to provide air defense cover for the fleet.
Moscow has used its naval power to blockade Ukrainian ports and threaten a potential amphibious landing along the coast. Without its flagship, its ability to menace Ukraine from the sea could be crippled.
It was the largest warship to be sunk during conflict since the British torpedoed Argentina's General Belgrano in the 1982 Falklands war.
KYIV TO SEE MORE ATTACKS
Russia's Defence Ministry said its forces would step up strikes on Kyiv.
"The number and scale of missile strikes on targets in Kyiv will increase in response to any terrorist attacks or acts of sabotage on Russian territory committed by the Kyiv nationalist regime," the Russian Defence Ministry said.
Kirill Kyrylo, 38, a worker at a car repair shop in the Ukrainian capital, said he had seen three blasts hit an industrial building, causing a blaze that was put out by firefighters.
"The building was on fire and I had to hide behind my car," he said, pointing out the shattered glass of the repair shop and bits of metal that had flown over from the burning building.
Moscow reported that Russian villages in the Belgorod region near the border had been hit by Ukrainian shelling. Attacks in the area, a major staging ground for Russia's invasion, could not be confirmed.
Russia initially described its aims in Ukraine as disarming its neighbor and defeating nationalists there.
Kyiv and its Western allies say those are bogus justifications for an unprovoked war of aggression that has driven a quarter of Ukraine's 44 million people from their homes and led to the deaths of thousands.
Ukrainian President Volodymyr Zelensky paid homage to all "those who halted the progress of the endless convoys of Russian military equipment ... Those who showed that Russian ships can go ... down to the bottom."
There were no immediate reports of damage following the explosions reported in Kyiv, Kherson in the south, the eastern city of Kharkiv and the town of Ivano-Frankivsk in the west.
Ukraine's armed forces said Russian attacks on the towns of Popasna and Rubizhne, both north of the port city of Mariupol, had been repulsed and a number of tanks and other armored vehicles had been destroyed. Reuters was not able to verify the reports.