Russia and Ukraine have been engaged in a series of deadly aerial attacks, with Sunday's strikes also coming a day after the Russian military said it had seized the Ukrainian village of Ivanivske, west of Bakhmut.
A militant attack on a Moscow concert hall on Friday that killed at least 133 people also became a new flashpoint between the two arch-rivals.
"Explosions in the capital. Air defence is working. Do not leave shelters," Kyiv mayor Vitali Klitschko posted on Telegram early Sunday.
The governor of the Lviv region, Maksym Kozytskyi, said the Stryi district, south of the city of Lviv, around 80 kilometres (50 miles) from the Polish border, was also attacked.
Officials in Kyiv, the surrounding Kyiv region and Lviv reported minor damage to some buildings but no casualties.
Temporary localised power cuts were also reported in the eastern Dnipropetrovsk region after an overnight drone attack.
Ukraine's air force said Russia had fired 29 cruise missiles and 28 drones at its territory overnight.
It said it had downed 18 of the missiles and 25 drones.
Russia has significantly escalated its air attacks against Kyiv in recent days, launching last week one of its largest aerial barrages against the country's energy sector since the start of the war.
"The enemy continues massive missile terror against Ukraine," Sergiy Popko, had of the Kyiv city military administration, posted on Telegram.
"It does not give up its goal of destroying Kyiv at any cost."
Polish airspace breach
US Ambassador to Ukraine Bridget Brink also noted the increased frequency of recent attacks.
"Russia continues to indiscriminately launch drones and missiles with no regard for millions of civilians, violating international law," Brink wrote on X.
Poland's army said Sunday that one of the Russian cruise missiles fired at western Ukraine had entered its airspace.
"Polish airspace was breached by one of the cruise missiles fired in the night by the air forces... of the Russian Federation," the army posted X.
"The object flew through Polish airspace above the village of Oserdow (Lublin province) and stayed for 39 seconds," it said.
The country's Armed Forces Operational Command (RSZ) had said earlier that its forces were on a heightened state of readiness because of the "intensive long-range aviation activity of the Russian Federation tonight" and the missile attacks in Ukraine.
Poland has been a staunch ally of Ukraine since Russia invaded in February 2022.
Kyiv, which has struggled to find weapons and soldiers after more than two years of war, has promised to retaliate to Moscow's strikes by taking the fighting to Russian soil.
Late on Saturday, Moscow said it had repelled a barrage of Ukrainian missiles fired at the city of Sevastopol in Crimea, which it seized from Ukraine in 2014.
Sevastopol's Moscow-appointed governor Mikhail Razvozhayev said rocket fragments had killed a 65-year-old resident, and four other people had been wounded.
"It was the biggest attack in recent times," he said.
Ukraine's army said Sunday that it had two Russian landing ships in an overnight strike on Sevastopol.
"The Ukrainian Armed Forces successfully struck the amphibious landing ships Yamal and Azov, a communications centre, and a number of the Black Sea Fleet's infrastructure sites," it said.
Ukraine has claimed to have destroyed about a thid of Russia's Black Sea fleet.
Territorial gains
On the battlefield, Russian forces are seeking to press their advantage in manpower and ammunition as Kyiv faces delays of additional Western aid.
Moscow claimed Saturday to have seized a village on the western outskirts of Bakhmut in eastern Ukraine.
Its capture last month of Adviivka, near the Russian-held stronghold of Donetsk, was the first major territorial gain made by Russia since the devastated city of Bakhmut was seized 10 months ago.
Russian President Vladimir Putin hailed that success as a sign that Russian forces were back on the offensive.
Putin has also sought to tie Kyiv to the Moscow concert hall attack, despite claims of responsibility by the Islamic State jihadist group, which also released graphic footage of the gunmen carrying out the attack.
Putin said four "perpetrators" were detained while trying to flee toward Ukraine, where they had made "contacts".
Kyiv has denied any involvement, saying that Russia was looking for excuses to step up the war.
The United States has said it has seen no sign of Ukrainian involvement in the Crocus City Hall attack.
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