The majority of Americans favor negotiations with Cuba that could lead to full diplomatic relations, according to a new Gallup Poll commissioned by a Washington research organization.

However, the American public also favors insisting on concessions from the Cubans as a price for opening such negotiations, the study found.

In general, the poll suggests, American hostility toward Cuba has declined over the years since Fidel Castro won power there, but U.S. suspicions of its closest Communist neighbor remain strong.

The poll was commissioned and released by Potomac Associates, a small think-tank here. It is one in a series of similar studies of public opinion and foreign policy.

The poll of 729 Americans showed that the public favors by 59 per cent to 25 per cent, "entering into negotiations with Cuba looking toward re-establishing diplomatic and economic relations and exchanging ambassadors."

However, by 46 per cent to 35 per cent, the sample said the United States should first insist that Cuba begin withdrawing its troops from Africa before beginning such negotiations. By 62 to 23 per cent, the sample felt the United States must also demand the release of all U.S. prisoners in Cuba as a precondition.

Despite those views, however, the Gallup sample said, by 60 to 20 per cent, that the United States "should take all legally possible steps to prevent anti-Castro Cubans in this country from terrorist actions against Cuba." (Where the figures in the poll results do not add up to 100, the difference had no opinion or said they didn't know the answer.)

The poll results are included in a study on the past and future of American-Cuban relations by Williams Watts and Jorge I. Dominguez. The study concludes that the state of American public opinion gives the Carter administration ample room to maneuver toward a better relationship with Cuba.