U.S. President Joe Biden walked around central Kyiv on an unannounced visit on Monday, promising to stand with Ukraine as long as it takes, on a trip clearly timed to upstage the Kremlin ahead of the one-year anniversary of Russia's invasion.

Biden, in trademark aviator sunglasses, and President Volodymyr Zelenskiy, in green battle fatigues, walked side-by-side to a gold-domed cathedral on a bright winter morning pierced by the sound of air raid sirens.

"When (Russian President Vladimir) Putin launched his invasion nearly one year ago, he thought Ukraine was weak and the West was divided. He thought he could outlast us. But he was dead wrong," Biden said.

"The cost that Ukraine has had to pay is extraordinarily high. Sacrifices have been far too great ... We know that there will be difficult days and weeks and years ahead."

Outside the cathedral, burnt-out Russian tanks stand as a symbol of Moscow's failed assault on the capital at the outset of its invasion. Its forces swiftly reached Kyiv's ramparts only to be turned back by unexpectedly fierce resistance.

Since then, Russia's invasion has killed tens of thousands of Ukrainian civilians and soldiers on both sides, cities have been reduced to rubble and millions of refugees have fled. Russia claims to have annexed nearly a fifth of Ukraine, while the West has pledged tens of billions of dollars in military aid to Kyiv.

The U.S. president promised a further $500 million worth of weaponry, including artillery ammunition, anti-armour systems and air defence radars, plus tighter sanctions on Russia.

"This visit of the U.S. president to Ukraine, the first for 15 years, is the most important visit in the entire history of Ukraine-U.S. relations," Zelenskiy said.

Foreign Minister Dmitro Kuleba called the visit a signal to Russia that "no one is afraid of you!"

It was clearly timed to upstage Putin, due to make a major address on Tuesday setting out aims for the second year of what he now calls a proxy war against the armed might of Washington and the transatlantic military alliance NATO.

"Of course for the Kremlin this will be seen as further proof that the United States has bet on Russia's strategic defeat in the war and that the war itself has turned irrevocably into a war between Russia and the West," said Tatiana Stanovaya, a Russian political analyst.