HAVANA, Jan. 21 -- 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 U.S.' 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 U.S. and Cuba can find opportunities to advance in our mutually shared interests," said Edward Alex Lee, a U.S. State Department official who led the immigration talks for the U.S.. " 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 U.S. federal law enacted in 1966, allows Cubans to get permanent residency after they have been present in the U.S. physically for at least one year; the wet foot/ dry foot policy allows Cubans who reach the U.S. shores to stay, but those who are stopped and caught at sea are returned to Cuba.

Josefina Vidal Ferreiro, director general of the U.S. Department with the Cuban Foreign Relations Ministry, hailed the " constructive" dialogue Wednesday, but criticized the persistence of the Cuban Adjustment Act and the wet foot/dry foot policy.

She said that those policies of the United States "contradict the spirit of the migration accords, and continue to be the main stimulus to the illegal migration, human traffic, and illegal entries into the United States of Cuban citizens."

"The Cuban delegation also noted that all the illegal Cuban migrants intercepted at sea are not returned to the island, which is contrary to the migration agreements in 1994 and 1995", Vidal said.

The meeting on Thursday will focus on discussion of the steps for normalization of relations, and the opening of embassies in Havana, the Cuban capital, and Washington, D.C., after half a century of being bitter foes, with the Cuban delegation to be headed by Vidal Ferreiro, and the U.S. delegation to be led by Roberta Jacobson, United States Assistant Secretary of State for Western Hemisphere Affairs and the top American diplomat for Latin America. Jacobson didn't participate in the immigration discussion. She is also the first assistant secretary of State to visit Cuba in nearly four decades.