Deputy Assistant Secretary for South America and Cuba Bureau of Western Hemisphere Affairs Alex Lee addresses the media during negotiations to restore diplomatic ties with Cuba in Havana January 21, 2015. [Photo/Agencies]

HAVANA -- Delegations of Cuba and the United States clashed vehemently over immigration policy Wednesday at the first session of a high-level meeting aiming to restore diplomatic relations between two countries.

The two-day meeting is the first high level conference held between Cuba and the United States since the surprising announcement on Dec. 17 by President Barack Obama and his Cuban counterpart Raul Castro about restoring the bilateral diplomatic ties broken off in January 1961.

At a press conference held at the close of Wednesday's meeting, leaders of two delegations acknowledged progress in several migration issues after the dialogue, but stressing that both sides maintained their contradictory views on the legality of the US' Cuban Adjustment Act and the wet foot/dry foot policy toward the island.

"The productive and collaborative nature of today's discussion proves that, despite the clear differences that remain between our countries, the US and Cuba can find opportunities to advance in our mutually shared interests," said Edward Alex Lee, a US State Department official who led the immigration talks for the US. " My government is fully committed to respecting the Cuban Adjustment Act, and the wet foot/dry foot policy will remain."

The Cuban Adjustment Act, a US federal law enacted in 1966, allows Cubans to get permanent residency after they have been present in the US physically for at least one year; the wet foot/ dry foot policy allows Cubans who reach the US shores to stay, but those who are stopped and caught at sea are returned to Cuba.