Biden aimed to consolidate a sharp improvement in relations since the island's conservative President Nicos Anastasiades took office last year pledging to forge a "strategic partnership" after decades of Greek Cypriot distrust of Washington.
For security reasons, the US vice president spent the night in the island's second city Limassol after flying in on yesterday evening.
But the streets of the capital Nicosia were already decked out in US flags ahead of his lunchtime meeting with Anastasiades at the presidential palace.
The breakaway state that Eroglu leads is recognised only by Turkey, whose troops occupied the island's northern third in 1974, and Biden moved swiftly on his arrival to reassure Greek Cypriots that the meeting signalled no change in US policy.
Washington recognises only "one legitimate government" in Cyprus, that led by Anastasiades, he said.
"My visit and meetings throughout the island will not change that."
Biden said he wanted to lend his support to the reunification which the rival Cypriot leaders relaunched in February but said the details of a settlement were for them to work out.
The international community has welcomed the new peace initiative, with greater input from Washington seen as enabling a breakthrough after two years of stalemate.
There has been no high-level US involvement in efforts to end the island's division since Greek Cypriots rejected a UN reunification plan in a 2004 referendum.
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