A senior American official says the United States is open to building a new relationship with Cuba.
However, Edward Alex Lee of the US State Department, who's been on an official visit to Cuba, stressed that any concessions must go hand-in-hand with more political freedom on the Caribbean island.
He said the two countries had held "very constructive" talks on migration and other issues this week.
But he declined to give any details of what he called "substantial progress".
Mr Lee, who has been on an official visit to Cuba, added the two nations would seek to continue these rare negotiations.
"Despite our historically difficult relationship...we have been able to speak to each other in a respectful and thoughtful manner," he told a news conference in Havana.
But he added that the US wanted a "fundamental change" in the Cuban government's attitude towards its own people.
"We want to have that opening reflect - from the Cuban side - a respect for Cubans to express themselves freely, to be able to petition their government with grievances without the danger of arrest."
The BBC reports talks between the two historic enemies were suspended in 2011 but resumed last July.
The main focus of the latest talks was migration: discouraging Cubans from risking their lives at sea to reach the US, by ensuring that there were safe and legal alternatives.