(Reuters) - U.S. airlines are proceeding with plans to launch new flights to Cuba this week despite doubts that President-elect Donald Trump has raised about the future of ties between the countries.

American Airlines Group Inc <AAL.O>, the world's largest airline, kicked off its first flight to Havana from Miami on Monday and intends to launch Charlotte-Havana service on Wednesday.

Its rival for Caribbean travel, JetBlue Airways Corp <JBLU.O>, has three new flights to Havana starting this week, with the first having departed from New York on Monday at 9:45 a.m. ET, according to tracking website FlightAware.com.

The new service comes as Trump said in a Twitter post on Monday that he will "terminate [the] deal" between Cuba and the United States if the communist-ruled island does not make an agreement that is better for the people of both countries.

The former Cold War foes began normalizing relations in December 2014 after 18 months of secret talks and have since restored full diplomatic ties.

They reached a memorandum of understanding that allowed U.S. airlines to start scheduled flights to Cuba after a half-century hiatus, and the Obama administration has eased travel restrictions for U.S. citizens - though general tourism remains illegal.

It was not immediately clear if Trump would target the aviation deal or other aspects of the detente. It also was unclear if there would be any impact from the death on Friday of Fidel Castro, who ousted U.S.-backed dictator Fulgencio Batista in Cuba's 1959 revolution.

"While we can't speculate, we are full steam ahead to begin service to Havana this week," said American Airlines spokesman Matt Miller. "We are proud to be the leading carrier between the U.S. and Cuba."

JetBlue spokespeople did not immediately comment on whether the airline was concerned that the incoming Trump administration would curtail its service to Cuba.

Scrapping the flights would throw a wrench in the plans of U.S. airlines, which expect an eventual payout from Cuban-Americans visiting relatives, leisure travelers desiring an experience that was once off limits, and executives buying business class fares to evaluate commercial opportunities in Cuba.

U.S. carriers have already been flying to lower-demand destinations in the island's provinces for months so they could establish a foothold there.

JetBlue was the first company to start service, with a flight on Aug. 31 from Fort Lauderdale, Florida to Santa Clara, a city in the central part of the island with a population of about 200,000 that is known for its monument to revolutionary leader Ernesto "Che" Guevara.

(Reporting By Malathi Nayak in New York and Jeffrey Dastin in Los Angeles; Editing by Alan Crosby)