Military vehicle in Donetsk. | Reuters

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Russian forces have fired missiles at several cities in Ukraine and landed troops on its south coast, 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."

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.