Speaking to TTG at WTM London, Juan Carlos Garcia Granda said steps taken by Washington since Donald Trump took office for the first time in 2017 have had a damaging effect on Cuba's tourism sector.
These measures are in addition to a US economic embargo on Cuba which has been in place for more than 60 years.
Garcia Granda believes if lines owned and operated by US-headquartered cruising giants like Royal Caribbean Group, Norwegian Cruise Line Holdings and Carnival Corporation were permitted to call into Cuba, huge numbers of passengers would soon follow.
Trump compounded the country's challenges earlier this year by adding Cuba to the list of State Sponsors of Terrorism when he started his second presidential term.
The move has a knock-on effect because UK tourists who have visited Cuba after 12 January 2021 are not eligible for an ESTA (the Electronic System for Travel Authorisation) to enter the US.
Garcia Granda said: "I will work every day to change the fact cruise ships don't generally come to Cuba. We are working with cruise lines that do not have a relationship with the US but almost all of the cruise companies are North American or have a relationship with the US. The message currently is if you visit Cuba, you cannot visit the US."
UK-based operator Ambassador Cruise Line is one of the few cruise lines which does call into Cuba. In late January, its Ambition ship stopped off in Havana and Santiago de Cuba. Ambassador's Ambience ship will visit Havana on 16 February next year.
"We could accommodate one, two or three million visitors if more cruise ships came to Cuba," Garcia Granda added, before joking: "We don't stamp the passports of arrivals. The British do not want to lie."