US Rep Raul Grijalba (D-ARIZ) (L) and US Senator Tom Udall (D-NM) talk after a news conference in Havana May 27, 2015. [Photo/Agencies]

Obama softened aspects of the embargo and called on Congress to end it during his State of the Union address in January.

Franken said there is strong support among the US public for normal relations.

"I think there is a very small minority, really, in the Senate and the Congress who have strong objections to this and I think that a majority of the American people and a majority of the Congress would be for lifting the embargo," he said. "But there is work to be done."

Some of that work emerged as the members of Congress spoke to reporters. Franken was asked about the presence of the US Navy base at Guantanamo Bay, Cuba, which Castro said must be returned to Cuba. Franken dodged the question, saying, "I don't believe that that is a salient issue at this time." He then added that he doesn't have a "strong opinion" on the base, though he supports closing the detention center there for terrorism suspects.

Udall was asked about the presence of criminals suspected of crimes in the United States who have found refuge in Cuba. The senator raised the example of Charlie Hill, who fled to the island after killing a police officer in New Mexico in 1971, and said he should be extradited.

"I assume with the normalization of relations we are going to have a lot more discussions about things like that," Udall said.