Biden will meet President Petro Poroshenko and Prime Minister Arseniy Yatsenyuk tomorrow, the one-year anniversary of the Maidan protests.
Yatsenyuk said earlier today that he hoped for an announcement on fresh US assistance to Ukraine during Biden's visit.
In September, the US announced a fresh USD 53 million aid package, including non-lethal military equipment, but Kiev wants Washington to go further and provide lethal assistance.
The secretary of Russia's national security council, Nikolai Patrushev, warned ahead of the trip that the conflict in east Ukraine "will grow" if America supplies Ukraine with weapons.
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Pro-Moscow separatist rebel and Ukrainian forces are fighting a drawn-out battle for territory in eastern Ukraine despite a tattered ceasefire agreed in September.
Russia denies giving military support to the separatists but relations between the Kremlin and the West have plunged to a post-Cold War low over the conflict.
In an interview with Kiev's The Day newspaper published today, Biden stressed there was "no military solution to this crisis" and accused Russia of "interfering in the affairs of a sovereign state".