Ukraine's military claimed on Thursday it had destroyed four Russian tanks on a road near the eastern city of Kharkiv, killed 50 troops near a town in Luhansk region and downed a sixth Russian aircraft, also in the country's east.
Russia has denied reports that its aircraft or armoured vehicles have been destroyed.
Ukraine's border guard service said that three of its servicemen had been killed in the southern Kherson region and that several more were wounded. Ukrainian troops have shot down five Russian helicopters, destroyed dozens of tanks and captured at least six troops in the first hours since Vladimir Putin ordered his forces to invade this morning. Kiev's military is far inferior to its Russian counterpart with an air defense system and air force date back to the Soviet era. But NATO and the US, despite deploying soldiers to neighbouring Romania in recent months, have made it clear that no troops will be sent and left the Ukrainian military to hold off the assault alone. By Thursday afternoon, battles were ongoing in Kiev, along the northern border with Belarus, in Luhansk and Donetsk in the east and around Kherson, the Dneiper River, and the port cities of Odessa and Mariupol in the south. Few expect Ukraine to emerge victorious from what is almost certain to be a prolonged, bloody, and vicious war - but so far, Kiev's forces have managed to inflict heavy losses on Putin's troops. Few expect Ukraine to emerge victorious from what is almost certain to be a prolonged, bloody, and vicious war - but so far, Kiev's forces have managed to inflict heavy losses on Putin's troops.
Russia's ground forces crossed into Ukraine from several directions, Ukraine's border guard service said, hours after President Vladimir Putin announced the launch of a major offensive.
Russian tanks and other heavy equipment crossed the frontier in several northern regions, as well as from the Kremlin-annexed peninsula of Crimea in the south, the agency said.
It said one of its servicemen died in a shelling attack along the Crimean border, the first officially confirmed military death of the Russian invasion.
Ukraine has suffered heavy casualties in its eight-year conflict with Russian-backed rebels in the separatist east, but has reported no fatalities along its southern border with Crimea for some years.
After holding a series of emergency calls with world leaders, including US President Joe Biden, the Ukrainian leader convened a meeting of the top military brass, his office said.
"The armed forces of Ukraine are waging heavy combat," presidential adviser Mykhailo Podoliak said. "We have losses," he added, without giving details.
"In several places, the Russian armed forces have been repelled."
Ukrainian officials said Russia was primarily targeting military infrastructure and silos, managing to push five kilometres deep along the norther frontier.
Russia says taking out military infrastructure at Ukraine's air bases
Russia's defence ministry said earlier it had taken out military infrastructure at Ukraine's air bases and "suppressed" its air defences, Russian news agencies reported.
The ministry denied reports that its aircraft had been downed over Ukraine. Earlier, Ukraine's military had said five Russian planes and one helicopter were shot down over its Luhansk region
"The air defence assets of the Ukrainian armed forces have been suppressed," Interfax news agency quoted the ministry as saying.
"The military infrastructure of the Ukrainian Armed Forces' air bases has been taken out of action.
"Information in foreign media about a Russian plane allegedly being shot down is not true."
The Russian defence ministry had said it was targeting Ukrainian military infrastructure with precision weapons after Putin announced a military operation against the country.
"Military infrastructure, air defence facilities, military airfields, and aviation of the Armed Forces of Ukraine are being disabled with high-precision weapons," the defence ministry said in a statement carried by Russian news agencies.
The statement comes after Russian President Putin authorised a military operation in eastern Ukraine on Thursday in what appeared to be the start of war in Europe over Russia's demands for an end to NATO's eastward expansion.
Shortly after Putin spoke in a special televised address on Russian state TV, explosions could be heard in the pre-dawn quiet of the Ukrainian capital of Kyiv. Gunfire rattled near the capital's main airport, the Interfax news agency said.
All responsibility for bloodshed will be on the conscience of the ruling regime in Ukraine: Russian President Vladimir Putin
Explosions also rocked the breakaway eastern Ukrainian city of Donetsk and civilian aircraft were warned away as the United States said a major attack by Russia on its neighbour was imminent.Putin said he had authorised a special military operation in breakaway areas of eastern Ukraine and clashes between Russian and Ukrainian forces were only a matter of time.
Hours earlier, pro-Russian separatists issued a plea to Moscow for help to stop alleged Ukrainian aggression - claims the United States dismissed as Russian propaganda.
Putin said he had ordered Russian forces to protect the people and demanded Ukrainian forces lay down their arms.
"All responsibility for bloodshed will be on the conscience of the ruling regime in Ukraine," Putin said.
He repeated his position that NATO expansion to include Ukraine was unacceptable and said Russia had been left with no choice but to defend itself against what he said were threats emanating from Ukraine.
The scope of the Russian military operation was not immediately clear. Moscow has long denied that it has plans to invade despite massing tens of thousands of troops near its neighbour.
Ukrainian President Volodymyr Zelenskiy said on Wednesday that Moscow had approved an offensive and had not replied to an invitation for talks.
"Today I initiated a telephone conversation with the President of the Russian Federation. The result was silence," he said.Later, Zelensky said Russia was attacking his country's "military infrastructure" and border guards, but urged citizens not to panic and vowed victory.
In a video message posted on Facebook after Putin announced the launch of a military operation against Ukraine, Zelensky also introduced martial law across the country, adding that he had spoken by phone with US President Joe Biden.
Meanwhile, Biden said his prayers were with the people of Ukraine "as they suffer an unprovoked and unjustified attack by Russian military forces".
"President Putin has chosen a premeditated war that will bring a catastrophic loss of life and human suffering. Russia alone is responsible for the death and destruction this attack will bring, and the United States and its Allies and partners will respond in a united and decisive way. The world will hold Russia accountable."
He said he would announce further sanctions on Russia on Thursday, in addition to financial measures imposed this week.
The Russian operations began as the U.N. Security Council held an emergency meeting on the Ukraine crisis in New York.
A draft resolution calling out Moscow over its actions toward its neighbour is doomed to fail due to Russia veto power, however a Security Council diplomat said it would put Russia on notice that it is "not in compliance with international law."