Live updates: follow the latest news on Russia-Ukraine
Up to 40 people have been killed in Russian attacks on Ukraine, an adviser to President Volodymyr Zelenskyy has said.
The adviser, Oleksii Arestovich, said several dozen people had been wounded.
Regional authorities in the southern port city of Odessa said 18 people were killed in a Russian missile strike.
At least six others were killed in the town of Brovary, near the capital Kiev, local authorities told Reuters.
The border guard said separately that Russian military columns have crossed the Ukrainian frontier into the Chernihiv, Kharkiv and Luhansk areas of Ukraine.
Russia's defence ministry said on Thursday it had taken out military infrastructure at Ukraine's airbases and “suppressed” its air defences, Russian news agencies reported.
The ministry denied reports that some of its aircraft had been shot down over Ukraine.
Ukraine's military said 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 and shot down a sixth Russian aircraft, also in the country's east.
Russia has denied reports its aircraft or armoured vehicles were destroyed.
“The air defence assets of the Ukrainian armed forces have been suppressed,” Interfax quoted the ministry as saying.
Russian forces were trying to capture the Chernobyl nuclear power plant, President Zelenskyy said on Twitter.
The plant was the site of the world’s worst nuclear accident when a nuclear reactor exploded in April 1986, spewing radioactive waste across Europe. The plant lies 130 kilometres north of Kiev.
The exploded reactor has been covered by a protective shelter to prevent radiation leak and the entire plant has been decommissioned.
Mr Zelenskyy said on Twitter that “our defenders are giving their lives so that the tragedy of 1986 will not be repeated.” He added that “this is a declaration of war against the whole of Europe.”
Earlier, explosions were heard in the Ukrainian capital Kiev. Blasts were also heard in Kharkiv and in the city of Odessa, agencies reported.
Kharkiv, Ukraine's second-largest city, is only 35km south of the Russian border and outside the eastern zone where Ukrainian forces have been battling Moscow-backed insurgents since 2014.
Ukraine and its allies condemned the operation, which the Ukrainian foreign minister called a “full-scale war".
Ukraine, a democracy of 44 million people with more than 1,000 years of history, is the biggest country in Europe by area after Russia.
It voted overwhelmingly for independence from Moscow after the fall of the Soviet Union and aims to join Nato and the European Union.
Russian military vehicles breached the Kiev region from Belarus to the north, Ukrainian officials said, after tanks reportedly rolled earlier into Ukraine from Crimea.
A senior Russian MP said Russia aims to ensure there is a pro-Moscow government in Kiev, pushing out US influence. President Putin has summoned tycoons to the Kremlin.
Mr Putin, who denied for months that he was planning an invasion, has called Ukraine an artificial creation carved from Russia by enemies, a characterisation Ukrainians call shocking and false.
Russia said it had so far targeted Ukraine's military infrastructure, air defence and air forces with high-precision weapons, and had not attacked Ukrainian cities, the Russian defence ministry said, according to RIA news agency.
The Russian president told other countries any attempt to interfere with the Russian action would “lead to consequences you have never seen in history”.
The Ukrainian president earlier rejected Moscow’s claims that his country posed a threat to Russia and made a passionate plea for peace.
US President Joe Biden said the world would “hold Russia accountable”, and Nato’s head called Russia’s actions a breach of international law and a threat to the security of Europe and its Atlantic allies.
British Prime Minister Boris Johnson has said a “vast invasion is under way by land, by sea and by air”, as he vowed to introduce more sanctions which would “hobble the Russian economy".
German Chancellor Olaf Scholz said Russia’s attack on the former Soviet nation had brought about a “dark day for Europe” and expressed his country’s “full solidarity with Kiev”. Mr Scholz said in Berlin that new sanctions would be imposed on Russia by Germany and its allies would show that “Putin has made a serious mistake with his war”.
Turkey called on Russia to halt what it described as “unfair and unlawful” actions in Ukraine.
A Turkish Foreign Ministry statement called the Russian attack “unacceptable” and said Turkey rejected it. The ministry warned the attack posed "a serious threat to the security of our region and of the world”.
Ukraine’s ambassador to the UK, Vadym Prystaiko, called for a no-fly zone to be put in place over his country.
Greece has urged France, which holds the rotating EU presidency, to call an emergency meeting of the bloc's energy ministers to discuss a collective response to surging energy prices, a trend now further exacerbated by Russia's attack on Ukraine.
Kostas Skrekas, the Greek Energy Minister, said the energy crisis had a "destructive impact" on the life of European citizens, on industries and economies. His letter dated February 24 was co-signed by his Bulgarian and Romanian counterparts.
"This is a crisis situation, which requires an EU level response," Mr Skrekas wrote in the letter addressed to French Ecological Transition Minister Barbara Pompili. "In this light, we would ask the French Presidency to organise an extraordinary meeting of the Council of Energy Ministers as soon as possible."
Ukraine declares martial law
Ukraine's President Zelenskyy announced the country will now be under martial law.
“We are working,” he told his people in a video message. “The army is working. Don't panic. We are strong. We are ready for everything. We will defeat everyone. Because we are Ukraine.”
Before Mr Putin’s announcement, world leaders worked to maintain a united stance and vowed to impose tougher sanctions in the event of an invasion.
Mr Putin’s declaration came even as the UN Security Council was in an emergency meeting on Wednesday night regarding the crisis, at Ukraine’s request.
Ukraine closed its civilian airspace overnight, citing a “potential hazard”, hours after a conflict zone monitor said airlines should stop flights because of the risk of aircraft being shot down or hit by cyberattacks.
The UN previously called for a ceasefire in eastern Ukraine, where sporadic fighting has taken place between Russian-backed separatists and the Ukrainian government since 2014.
Lt Col Tyson K Wetzel, the 2021-2022 senior US Air Force fellow at the Atlantic Council's Scowcroft Centre for Strategy and Security, said he believed Ukrainians had strong defences.
“I think they’re going to trade space for time and potentially do a retrograde and allow the Russian forces to come in, and do ambushes, bloody tactics. I think this will be very costly for the Russians in the medium term. I’m dubious of them being able to take the entire country. I don’t think this is going to be happening in the first three to five days of the conflict,” Mr Wetzel said.
Ukrainian MP Lesia Vasylenko said Russian troops were moving “inward into Ukraine” after breaching borders.
On Thursday people arrived in the Polish village of Medyka, close to the Ukrainian border, after fleeing the violence.
Mariusz Kaminski, Poland’s Minister of Internal Affairs, said the country had for weeks been bracing for a “wave of refugees” and would “do everything possible to make those in need find a shelter.”
EU plans ‘strongest package’ of sanctions
The European Union is planning at an emergency session on Thursday the “strongest, the harshest package” of sanctions it has ever considered.
“We will freeze Russian assets in the European Union and stop the access of Russian banks to European financial markets,” European Commission President Ursula von der Leyen said at a news conference on Thursday morning. “These sanctions are designed to take a heavy toll on the Kremlin's interests and their ability to finance war. And we know that millions of Russians do not want war.”
Russian assets nosedived as military attacks across Ukraine prompted emergency central bank action and investors braced for the toughest round of Western sanctions yet.
More than $250 billion was lost in stock market value.
The rouble sank to a record low and stocks collapsed 45 per cent — their biggest retreat.
Russian Eurobonds plummeted, pushing some into distressed territory.
The Bank of Russia said it will intervene in the foreign exchange market for the first time in years and take measures to tame volatility in financial markets.
Kiev government closes schools and looks to open bomb shelters
Under the new martial law order in Ukraine, schools and nurseries will be closed and the country's entire hospital and medical system will be working in intensified mode.
The government is looking into opening bomb shelters around the capital.
According to a memo, all those not working in critical roles should stay at home and be prepared to go to shelters should sirens sound.
The government released a map directing residents to various shelters around the city.
People queued to withdraw money and buy supplies of food and water in Kiev. Traffic was jammed going west out of the city towards the Polish border.
Western countries have been preparing for the likelihood of hundreds of thousands of Ukrainians fleeing an assault.