HAVANA/WASHINGTON, April 20 (Reuters) - U.S. officials met this month with their Cuban counterparts in Havana, officials from both countries said on Monday, as Washington pushes for reforms of Cuba's state-led economy amid an energy crisis and a U.S. blockade on oil shipments to the island.

A U.S. State Department official confirmed that the meeting took place on April 10 for talks overseen by Secretary of State Marco Rubio, without detailing which officials took part in the talks. The meeting was first reported by Axios.

"The delegation reiterated that the Cuban economy is in free fall and that the island's ruling elites have a small window to make key U.S.-backed reforms before circumstances irreversibly worsen," the official said in comments shared on condition of anonymity.

The talks were a sign that the two countries could reach a diplomatic agreement even though President Donald Trump has hinted at potential military action against the island following the U.S. raid in January that captured President Nicolas Maduro of Venezuela, a close ally of Cuba. 

The plane carrying the American delegation was the first U.S. government aircraft to land in Cuba proper since 2016, not counting the U.S. base at Guantanamo Bay, the official said.

"President Trump is committed to pursuing a diplomatic solution, if possible, but will not let the island collapse into a major national security threat if Cuba's leaders are unwilling or unable to act," the official added.

Alejandro Garcia del Toro, who handles U.S. affairs in the Cuban foreign ministry, said neither party set deadlines or made threatening statements in the meeting, which he called "respectful."

"Eliminating the energy embargo against the country was a top priority for our delegation," Garcia del Toro said.

U.S. proposals include allowing Elon Musk's Starlink internet terminals in the country, compensation for U.S. persons and corporations for assets confiscated by Cuba after the 1959 revolution, the release of political prisoners, and allowing greater political freedoms, the official said. The U.S. is also concerned about the influence of foreign powers on the island, the official said.

Garcia del Toro said that the U.S. was represented by midlevel State Department officials and Cuba was represented "at the level of deputy foreign minister."

A senior State Department official also met separately with Raul Guillermo Rodriguez Castro, grandson of former Cuban President Raul Castro, who is 94 and still wields great influence, the official said.