A week after an effort to gain the release of an American jailed in Cuba ended in recriminations, the Cuban foreign minister said Friday that the door remained open to free him on humanitarian grounds, but only with a reciprocal effort from the United States.

In an interview with editors and reporters at The New York Times, Foreign Minister Bruno Rodríguez Parrilla said his country was still seeking closer ties with the United States, suggesting that the two sides start with subjects on which they should be able to find common ground most easily — fighting drug trafficking, terrorism and threats to the environment, to name a few.

“It’s in the best interest of the U.S. and Cuba to move ahead on the normalization of bilateral relations,” Mr. Rodríguez said.

One of the more contentious issues roiling relations right now is the dispute over Alan Gross, a State Department contractor serving a 15-year sentence in Cuba for distributing satellite equipment under an American program aimed at weakening the Cuban government.