The United States and Cuba are trying to eliminate obstacles to normalized ties as the highest-level U.S. delegation to the communist island in more than three decades holds a second day of talks with Cuban officials.

U.S. objectives during Thursday’s session include the lifting of restrictions on American diplomats in Cuba and assurances that Cubans will have unfettered access to a future U.S. Embassy in Havana. The Americans say the resumption in full diplomatic relations depends on how quickly its requests are met. Cuba is demanding its removal from a U.S. list of state sponsors of terrorism, which Washington says it is considering.

On Wednesday, the U.S. said it dispatched additional ships to the Florida Straits to halt Cuban rafters but rebuffed demands for broader changes to U.S. migration rules that grant virtually automatic legal residency to any Cuban who touches U.S. soil.

Cuba’s government blames the Cold War policy for luring tens of thousands of Cubans a year to make perilous journeys by land and sea to try to reach the United States. Still, many Cubans are worried the elimination of the rules would take away their chance to have a better life in the U.S.

In Washington, U.S. Homeland Security Secretary Jeh Johnson said America’s “wet foot, dry foot” approach, which generally shields Cubans from deportation if they reach U.S. territory, remains in effect. But he stressed that those trying to come illegally would most likely be interdicted and returned.

U.S. officials reported a spike in the number of rafters attempting to reach Florida after the Dec. 17 announcement that the countries would move to normalize ties. Those numbers appear to have slowed in recent days.

“Cuba wants a normal relationship with the U.S., in the broadest sense but also in the area of migration,” said Cuba’s head of North American affairs, Josefina Vidal. She called for the U.S. to end “exceptional treatment that no other citizens in the world receive, causing an irregular situation in the flow of migrants.”

American officials instead pressed Cuba to take back tens of thousands of its nationals whom U.S. authorities want to deport because they have been convicted of crimes. No progress was made on that issue, according to an official present in the meeting. The official wasn’t authorized to speak on the matter and demanded anonymity.

The talks Thursday are expected to focus on the broader question of how the U.S. and Cuba can end a half-century of enmity — as promised by Presidents Barack Obama and Raul Castro last month. The nations hope to re-establish embassies and post ambassadors to each other’s capitals in the coming months.

After meeting with the Cubans for more than three hours, the State Department’s Alex Lee said the “discussions prove that despite clear differences that remain between our countries, the United States and Cuba can find opportunities to advance our mutual, shared interests as well as engage in respectful and thoughtful dialogue.”

Lee led the U.S. delegation ahead of Wednesday afternoon’s arrival of Roberta Jacobson, the top American diplomat for Latin America and most senior U.S. official to visit Cuba since 1980.

Lt. Cmdr. Gabe Somma, spokesman for the Coast Guard’s 7th District in Miami, said “aggressively” stepped-up patrols have eased the increase in rafters seen immediately after the twin announcements last month by Castro and Obama.

“We have seen a slowdown in the last two weeks,” he said.

(AP)