Russian paratroopers entered Kharkov, Ukraine's second largest city, on the 2nd, AFP news agency reported, citing Ukrainian military announcements.
According to reports, the Ukrainian military said via Telegram that Russian paratroopers entered eastern Kharkov on the same day and attacked a local hospital, and the fighting continued.
"Russian paratroopers landed in Kharkov and attacked a local hospital," the Ukrainian military said in a statement distributed via Telegram.
This move came as Russia, which launched an invasion of Ukraine on the 24th of last month, faltered in initial resistance, but raised its firepower on the 1st and began to bombard civilians indiscriminately, regardless of their residences.
Located in eastern Ukraine and close to the Russian border, Kharkov is known to have a population of 1.4 million, the majority of which are Russian-speaking.
There are also reports that the city of Kherson with a population of 250,000 in southern Ukraine has been occupied by Russian forces.
According to local media, Mayor Igor Kolikaev Kherson said Russian troops had seized the train station and port overnight.
Mayor Kolikaev said: "The fighting is going on and the occupation of our city is taking place."
At least 100 people were injured in the attack by Russian forces in the port city of Mariupol in the southern Sea of Azov, local media reported, citing Mayor Vadim Wojchenko.
According to AFP and BBC reports, two apartments were destroyed by Russian airstrikes in Borodyanka, about 50 kilometers from Kyiv.
In the northwestern region of Zitomir, an air strike presumed to be a missile attack caused a fire in a residential area, killing four people.
A long convoy of Russian troops moving towards Kyiv was witnessed in an area only 24 km northwest of Kiev.
Ukrainian officials also said Russian troops attacked a TV tower near a broadcasting station in Kyiv, killing five people.