Shortly after arriving, he met with Ukrainian President Volodymyr Zelensky, according to broadcaster CNN.
During his visit, Biden was expected to pledge further support for Ukraine, including critical equipment such as artillery ammunition, anti-armor systems, and air surveillance radars, according to an announcement.
Biden said in a tweet: "As we approach the anniversary of Russia’s brutal invasion of Ukraine, I'm in Kyiv today to meet with President Zelenskyy and reaffirm our unwavering commitment to Ukraine’s democracy, sovereignty, and territorial integrity."
He added: "When 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 also pledged to continue supporting Ukraine as it defends itself from Russian aggression.
"Over the last year, the United States has built a coalition of nations from the Atlantic to the Pacific to help defend Ukraine with unprecedented military, economic, and humanitarian support – and that support will endure," Biden said in his Twitter message.
'An extended discussion on our support for Ukraine'
In a statement posted by the White House, Biden said: "Today, in Kyiv, I am meeting with President Zelenskyy and his team for an extended discussion on our support for Ukraine."
He added: "I will announce another delivery of critical equipment, including artillery ammunition, anti-armor systems, and air surveillance radars to help protect the Ukrainian people from aerial bombardments. And I will share that later this week, we will announce additional sanctions against elites and companies that are trying to evade or backfill Russia’s war machine."
Air raid sirens blared across the Ukrainian capital as Biden visited the city but there were no reports of Russian missile or air strikes, the Reuters news agency reported.
'I look forward to traveling on to Poland'
Biden is scheduled to visit Poland on Tuesday and Wednesday.
He said in his statement on Monday that he looked forward "to traveling on to Poland to meet President Duda and the leaders of our Eastern Flank Allies, as well as deliver remarks on how the United States will continue to rally the world to support the people of Ukraine and the core values of human rights and dignity in the UN Charter that unite us worldwide."
Polish President Andrzej Duda has said in a media interview that he will ask Biden to send more American soldiers and military equipment to Poland when the US leader visits Warsaw this week amid Russia's invasion of neighbouring Ukraine.
The US ambassador to Poland, Mark Brzezinski, said last week that Biden would deliver a key speech to the Polish people on Tuesday afternoon in the gardens of Warsaw’s Royal Castle.
The US embassy in Warsaw has said that Biden will on Tuesday "deliver remarks ahead of the one-year anniversary of Russia’s brutal and unprovoked invasion of Ukraine, addressing how the United States has rallied the world to support the people of Ukraine as they defend their freedom and democracy, and how we will continue to stand with the people of Ukraine for as long as it takes."
Russia invaded Ukraine on February 24, 2022.
Monday is day 362 of Russia's war in Ukraine.
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Source: IAR, PAP, Reuters, CNN, TVP Info