Russian forces fired missiles at several cities in Ukraine and landed troops on its south coast on Thursday, officials and media said, after President Vladimir Putin authorised what he called a special military operation in the east.
Shortly after Putin spoke in a 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, and sirens were heard over the city.
"Putin has just launched a full-scale invasion of Ukraine. Peaceful Ukrainian cities are under strikes," Ukrainian Foreign Minister Dmytro Kuleba said on Twitter.
"This is a war of aggression. Ukraine will defend itself and will win. The world can and must stop Putin. The time to act is now."
US President Joe Biden, reacting to an invasion the United States had been predicting for weeks, said his prayers were with the people of Ukraine "as they suffer an unprovoked and unjustified attack by Russian military forces".
Russia has demanded an end to NATO's eastward expansion and Putin repeated his position that Ukrainian membership of the US-led Atlantic military alliance was unacceptable.
He said he had authorised military action after Russia had been left with no choice but to defend itself against what he said were threats emanating from modern Ukraine, a democratic state of 44 million people.
Ukrainian President Volodymyr Zelenskiy said Russia had carried out missile strikes on Ukrainian infrastructure and border guards, and that explosions had been heard in many cities.
He said that martial law had been declared and that he had spoken by telephone to Biden. Reservists were called up on Wednesday.
Media reported that military command centres in Kyiv and the city of Kharkiv in the northeast had been struck by missiles while Russian troops had landed in the southern port cities of Odessa and Mariupol.
A Reuters witness later heard three loud blasts in Mariupol.
Russian-backed separatists said they had launched an offensive on the Ukrainian-controlled town of Shchastia in the east, Russia's Interfax news agency said, and explosions also rocked the breakaway eastern Ukrainian city of Donetsk.
Hours earlier, the separatists issued a plea to Moscow for help to stop alleged Ukrainian aggression - claims the United States dismissed as Russian propaganda.
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