Andrew Cuomo has become the first US state governor to visit Cuba since a thaw in relations began last year.
Mr Cuomo led a delegation of business executives from New York state to the island where he held talks with the Cuban minister for external trade.
He said that the isolation of Cuba had not worked.
Relations between the US and Cuba have improved since the announcement in December that the two countries would work towards restoring diplomatic ties.
US President Barack Obama and his Cuban counterpart, Raul Castro, met earlier this month at a regional summit in Panama.
Days after the meeting, President Obama recommended that Cuba should be removed from the list of states the US government considers to be sponsors of terrorism.
A number of US officials and politicians have visited the Communist-run island since the thaw in relations was announced on 17 December, but Mr Cuomo is the first state governor to do so.
He travelled with a delegation of New York-based companies which he said he hoped would become some of the first to operate in Cuba.
Mr Cuomo also said engagement and full relationships were the best way “to have a dialogue on the issues that we agree with and the issues that we disagree about”.
The BBC’s Will Grant in Havana says US politicians are keen to be seen in a country that was until very recently off-limits and to show their support for the move to normalise ties.