Sun Country Airlines is throwing in the towel on scheduled flights to Cuba, citing shaky demand and restrictions on travel to the island.

The privately held Minnesota-based airline told the U.S. Department of Transportation in a motion earlier this month that it would relinquish its rights to operate the scheduled flights to Santa Clara and Matanzas, from Minneapolis-St. Paul.

The Trump administration on Wednesday released a list of restrictions that would make it more difficult for U.S. citizens to travel to the island, including ending individual, so-called "people-to-people" cultural exchanges that were permitted under loosened rules introduced by the Obama administration.

Instead, travelers who want to visit Cuba for nonacademic, people-to-people exchanges will have to travel in a group run by an organization that is subject U.S. jurisdiction, and accompanied by a representative of the sponsoring organization, the new rules say.

The rules take effect on Thursday. President Donald Trump in June called for an end to some of the recently loosened travel regulations.

U.S. commercial carriers rushed to get permission to start commercial flights to the island, the first such flights in more than 50 years, landing on the island with a fanfare of water-cannon salutes.

But demand for flights to some smaller Cuban cities has been weaker than what some carriers anticipated, as key lodging infrastructure is lacking compared with other Caribbean destinations that are easier for American tourists to visit.

"Sun Country Airlines is no longer considering operating scheduled service from Minneapolis/St. Paul to Cuba due to continued regulatory and market uncertainties," a Sun Country Airlines spokeswoman told CNBC.

Other airlines have scaled back on service to Cuba or canceled the routes altogether amid high competition and lackluster demand to meet the supply of flights. Silver Airways called off flights to the island, citing competition from larger carriers. Spirit Airlines announced earlier in the year it was ending its flights to Cuba.

American Airlines last year cut the number of its daily flights to Cuba from 13 to 10, a few months after it launched service to the island. This winter, it will cut a flight from Miami to Cienfuegos, bringing the daily total to nine, a decision made earlier this year, a spokesman said.

Spokespeople for Delta Air Lines and Southwest Airlines, which both offer flights to Havana, said they are reviewing the new restrictions.

The new Trump administration restrictions also prohibit American travelers from staying in more than 80 Cuban hotels.

For its part, home-sharing giant Airbnb said it was also reviewing and planned to comply with the new regulations.