Carnival Corporation gained approval to launch limited cruises to Cuba as early as May 2016, the company said Tuesday.

The week-long trips, which were cleared and licensed by the Treasury Department and Commerce Department, will be under the company's newly launched social impact travel brand dubbed "fathom," which will also include similar trips to the Dominican Republic.

The trips will allow American travelers to go to Cuba for "cultural, artistic, faith-based and humanitarian exchanges," according to Carnival.

The weekly seven-day voyages will begin in April 2016, the company said, and launch from Miami. After the first inaugural trip to the Dominican Republic, trips to Cuba will be added in May 2016.

"We are excited about receiving U.S. approval as the very important first step to ultimately take travelers to Cuba under the existing 12 criteria for authorized travel. We look forward to working with the Cuban authorities for their approval to help make the social, cultural and humanitarian exchanges between U.S. citizens and the people of Cuba a reality," Arnold Donald, president and CEO of Carnival, said in a statement Tuesday.

Trips to the Dominican Republic will start at $1,450 per person, while those to Cuba will start at $2,990 per person, Carnival said. The Cuban government still has to approve the trips, however.

Carnival's efforts come as the Obama administration works to normalize diplomatic relations with Cuba after they were severed more than 50 years ago. Last week, the White House announced the two countries would be re-opening embassies in each other's capitals, and earlier this year, the administration announced it would make travel to Cuba as easy as possible for people under the 12 categories of travel allowed under the embargo.

Obama said that only "general" licenses would be needed to travel to Cuba for family visits, education, cultural exchanges or other approved reasons. That means those trips and their itineraries don't have to be pre-approved by the government.

Many Republicans have argued that these sorts of visits are essentially tourism disguised as cultural exchanges, and have been working to undermine them through legislation this year. For example, Republicans are hoping to pass language in the financial services appropriations bill later this year that would terminate "people-to-people" exchanges, which GOP members say has devolved into tourism.

Language in a transportation bill would also make it illegal for any new vessels traveling to Cuba to benefit from former U.S. property that was confiscated by Cuba decades ago when Fidel Castro came to power.