Russia attacked Ukraine overnight into Tuesday, Polish Radio's IAR news agency reported.
In Kyiv, missiles and missile debris hit residential buildings in several districts, killing at least one person, according to city authorities.
A further seven people were injured, including a child, the polskieradio24.pl website reported.
In Kharkiv, a Russian rocket struck a block of flats, killing two residents and injuring others, according to officials.
Russian missiles also hit other facilities, including a boarding school, the IAR news agency reported.
Meanwhile, one person was killed in a Russian rocket attack on the central city of Pavlohrad, according to polskieradio24.pl.
Andriy Yermak, chief of staff to Ukraine's President Volodymyr Zelensky, said that "Russian terror can only be stopped by force," adding that otherwise, after Ukrainian cities today, tomorrow its next target would be Western cities, as cited by Polish Radio.
In the past 24 hours, Ukrainian and Russian forces clashed 68 times in battlefield engagements, according to the General Staff in Kyiv.
Russia carried out three missile strikes, 65 air attacks, and 56 strikes using multiple-launch rocket systems, polskieradio24.pl reported.
Russia targeted over 140 settlements in Ukraine's Chernihiv, Sumy, Donetsk and Luhansk regions, as well as around the cities of Zaporizhzhia, Dnipro, Kherson and Mykolaiv, according to military officials in Kyiv.
Meanwhile, there were intense battles near the eastern city of Avdiivka, where Ukrainian forces repelled 10 Russian attacks, and near Marinka, where there were over 20 clashes over the last 24 hours, polskieradio24.pl reported.
Meanwhile, Ukraine's air force on Monday struck eight concentrations of Russian troops, according to the General Staff in Kyiv.
Ukraine also fired missiles into a Russian command post, a Russian artillery system and a Russian radar station, polskieradio24.pl reported.
On Tuesday morning, the Polish Army said it had scrambled its jets as well as NATO aircraft, due to a "heightened activity" by the Russian air force aimed against Ukraine.
Poland's military said it had taken all necessary steps to protect the country's airspace and was monitoring the situation "on a continuous basis."
Tuesday is day 699 of Russia’s war on Ukraine.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
Source: IAR, polskieradio24.pl, General Staff of the Armed Forces of Ukraine
