Cuba has said it will lift a ban on Cubans and Cuban Americans entering and leaving the Caribbean island by commercial vessels, opening the way for the cruise operator Carnival to set sail for the country next week.

Carnival’s 1 May cruise, the first from the US to the Communist-run country since the 1959 revolution, was thrown into doubt when the company triggered a backlash by refusing Cuban Americans passage due to a cold war-era law.

A statement carried by state-run media said that from Tuesday Cuban citizens would be authorised “independently of their migratory status to enter and leave as passengers and crews of cruise ships”.

Carnival received approval from the US last year to sail to Cuba, and the green light from Havana a day after Barack Obama’s historic visit to the country in March.

The waters between the two countries have been the scene of mass migration as well as hijackings and other crimes in the past, leading Cuba to ban Cubans from travelling by boat without special permission. Restrictions on travelling by air were lifted years ago.

Protests in Miami, where the company is based, a discrimination lawsuit and criticism by the secretary of state, John Kerry, led Carnival to start accepting bookings from Cuban Americans this month.

The company said it would postpone the cruise if necessary, but also expressed confidence that Cuba would rescind the law in time. It is expected to begin sailing to three Cuban cities every fortnight from 1 May.

Cuban-born Americans are free to enter their homeland by air, with about 300,000 arriving every year.

The statement on Friday said authorities were reviewing a ban on citizens boarding recreational vessels such as fishing boats and yachts.