President Volodymyr Zelenskyy, meanwhile, marked Ukraine's Statehood Day by reaffirming the country's sovereignty – a rebuke to Russian President Vladimir Putin, who used his claim that Ukraine didn't exist as a nation to justify his invasion.
"Now, like more than a thousand years ago, our civilizational choice is unity with the world," Zelenskyy said in a speech on a square outside St. Michael's Monastery in Kyiv.
"To be a power in world history. To have the right to its national history – of its people, its land, its state. And of our children – all future generations of the Ukrainian people. We will definitely win!"
He also honored servicemen and handed out first passports to young citizens as part of ceremonies. The holiday coincides with commemorations of the adoption of Christianity on lands that later became Ukraine, Russia and Belarus.
The Russian Defence Ministry said it shot down a Ukrainian missile in the city of Taganrog, about 40 kilometres east of the border with Ukraine, and local officials reported 20 people were injured, identifying the epicenter as an art museum.
Debris fell on the city, the ministry added, alleging the missile was part of a "terror attack" by Ukraine.
Oleksiy Danilov, Ukraine's secretary of the National Security and Defence Council, blamed Russian air defense systems for the explosion.
Russia's Defence Ministry said it downed a second Ukrainian missile near the city of Azov, which like Taganrog is in the Rostov region, and debris fell in an unpopulated location.
Earlier in the day, a Ukrainian drone was shot down outside Moscow, the Defence Ministry said, in the third drone strike or attempt on the capital region this month. The ministry reported no injuries or damage in the latest incident, and it didn't give an exact location where the drone fell.
Since the war began, Russia has blamed Ukraine for drone, bomb and missile attacks on its territory far from the battlefield's front line. Ukrainian officials rarely confirm being behind the attacks, which have included drone strikes on the Kremlin that unsettled Russians.
The strikes have hit Russian ammunition and fuel depots, as well as bridges the Russian military uses to supply its forces, and military recruitment stations. The attacks have also included killings of Russian-appointed officials on occupied Ukrainian territory.
Three months ago, a Russian warplane accidentally dropped a bomb on Belgorod, injuring two people, in an incident where Ukraine was initially suspected.
Meanwhile, the commander of Ukraine's armed forces, Col.-Gen. Oleksandr Syrskyi, said his troops were pushing forward in parts of eastern Ukraine occupied by Russia and meeting stiff resistance as the war drags into its 18th month.
"The enemy fiercely clings to every centimeter, conducting intense artillery and mortar fire," he said in a statement.
Recent fighting has taken place at multiple places along the more than 1,000-kilometre front, where Ukraine deployed its recently acquired Western weapons to push out the Kremlin's forces. However, it is attacking without vital air support and faces a deeply entrenched foe.
A Western official said Thursday that Ukraine had launched a major push in the southeast. Putin acknowledged that fighting has intensified there, but insisted Kyiv's push has failed.
Zelenskyy posted a video on Thursday night in which Ukrainian soldiers said they had taken Staromaiorske in the Donetsk region. Russian military bloggers said artillery fire at the Ukrainian troops had effectively razed the village and reported more barrages on Friday.
Capturing the village, which in 2014 had a population of 682, would give Ukraine a platform to push deeper into Russian-held territory, the bloggers noted.
The area has been a focus of Ukraine's counteroffensive since June, and its troops have previously captured several other villages there as they slowly work their way across extensive Russian minefields.
It was not possible to verify either side's claims about what is happening in the war zone.
Syrskyi said fighting that targets the enemy's artillery as well as its command and control structure is a priority as his troops probe Russian lines for weaknesses.
"In these conditions, it is crucial to make timely management decisions in response to the situation at hand and take measures for maneuvering forces and resources, shifting units and troops to areas where success is evident, or withdrawing them from the enemy's fire," he said.
Russia is trying to hold on to the territory it controls in the four provinces it illegally annexed in September – Zaporizhzhia, Donetsk, Kherson and Luhansk.
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