The attack came on the first day of an invasion of Ukraine that President Vladimir Putin launched
Russia said Thursday that its military had destroyed more than 70 military targets, including 11 airfields in Ukraine.
"As a result of strikes carried out by the Russian armed forces, 74 Ukrainian military ground facilities were destroyed," said Igor Konashenkov, a defence ministry spokesman.
Destroyed facilities included 11 airfields, three command posts and 18 radar stations of the S-300 and Buk-M1 anti-aircraft missile systems, he said.
He added that a Ukrainian military helicopter and four drones had also been shot down.
Konashenkov said separatist forces continued an offensive backed by air support of the Russian armed forces.
Currently "armed groups of nationalists" are putting up resistance, he said, claiming that Ukrainian troops wanted to leave the area of hostilities.
He said that Defence Minister Sergei Shoigu had ordered Russian troops to "treat Ukrainian servicemen with respect".
Putin launched an offensive on Ukraine in the early hours of Thursday after a national address aired at around 5:40 am local time.
Shortly afterwards, the first bombardments were heard in Ukraine's capital, Kyiv, and several other cities, according to AFP correspondents.
At least 68 people were killed, including both soldiers and civilians, according to an AFP tally from various Ukrainian official sources.
In the deadliest single strike reported by the authorities, 18 people were killed at a military base near Ukraine's Black Sea port city of Odessa.
Ukraine's border guards said Russian forces had reached the region around the capital, Kyiv.
An AFP reporter in the northern part of the city saw several low-flying helicopters overhead amid reports that an airfield was under attack.
Ukrainian Foreign Minister Dmytro Kuleba said a "full-scale invasion" was underway.
President Volodymyr Zelensky declared martial law and said Russia was attacking his country's "military infrastructure" but urged citizens not to panic and vowed victory.