Led by Senator Tom Udall, the group of Democratic lawmakers was on a mission in an attempt to strengthen ties between the former Cold War foes following decades of enmity.

That animosity has been buttressed by an economic embargo in place since 1962 that bars trade between the two nations.

U.S. Congress would have to pass legislation in order to lift the embargo.

Minnesota Senator Al Franken said there were few American lawmakers that would block the move.

“I think that it’s a very small minority, really, in the Senate, in the Congress, who have a strong objection,” Franken said, speaking of those who might object to lifting the sanctions.

U.S. President Barack Obama has asked the Republican-run U.S. Congress to vote to end the embargo.

Udall, of New Mexico, said several bills were on the way to address the matter.

“There’s growing bipartisan support in the Senate for all of these bills… whether it’s dropping agriculture restrictions, whether it’s lifting the travel bans, whether it’s the Internet,” he said.

He said he thought there was “great support” among Americans to lift the ban, but warned it could take time.

“It doesn’t mean it’s going to happen tomorrow… but the steps are taking place,” he said.

Franken joined his cautious optimism.

“I think the majority of the Congress will be for lifting the embargo, but there’s work to do,” he said.

In town since Saturday, they were joined by fellow lawmakers John Larson (Connecticut) and Raul Grijalva (Arizona), for talks with foreign ministry and trade officials.

Obama and President Raul Castro announced in December their countries would seek to restore diplomatic relations.

Castro and Obama also held a historic meeting in Panama in April on the sidelines of a regional summit.