WASHINGTON (Reuters) - The Trump administration on Saturday imposed U.S. travel sanctions on a second high-level Cuban official as it increased pressure on its old Cold War foe and Havana’s ongoing support of Venezuela’s socialist president, Nicolas Maduro.

U.S. Secretary of State Mike Pompeo said the United States would bar entry for Cuban Interior Minister Julio Cesar Gandarilla Bermejo, citing what he called the minister’s involvement “gross violations of human rights in Venezuela.”

He called for other countries to join the United States in holding Havana to account.

In announcing the largely symbolic move, Pompeo said Gandarilla Bermejo was also responsible for “arbitrarily arresting and detaining thousands of Cuban citizens and unlawfully incarcerating more than 100 political prisoners in Cuba”.

His ministry had overseen the torture of political dissidents, detainees and prisoners, as well as the murder of some of these individuals by police and security forces, Pompeo said in a statement on Saturday.

Washington in September imposed similar U.S. travel sanctions on Cuban Communist Party chief Raul Castro, Cuban’s former president and younger brother of the late Fidel Castro, over his support for Maduro and involvement in what it called “gross violations of human rights.”

In addition to Gandarilla Bermejo, the State Department said it would block entry to his children, Julio Cesar Gandarilla Sarmiento and Alejandro Gandarilla Sarmiento.

The Cuban government has strongly rejected such accusations in the past. No immediate comment was available from Havana.

“The Castro regime’s repression of human rights and fundamental freedoms in both Cuba and Venezuela necessitates worldwide concern and a louder international call to action,” Pompeo said in a statement.

“We strongly encourage other governments and international organizations demand accountability of the Cuban government for violating and abusing human rights and fundamental freedoms.”

The sanctions are the latest in a series of punitive measures that Trump has taken against Cuba since taking office in 2017, as he rolls back the historic opening to Havana under his Democratic predecessor, Barack Obama.

Cuba’s support for Maduro has been a flashpoint. The United States and dozens of other countries earlier this year recognized opposition leader Juan Guaido as Venezuela’s rightful president, but Maduro retains the support of China and Russia.

Maduro has accused Guaido - who earlier this year assumed an interim presidency after alleging that Maduro had rigged the last election - of trying to mount a U.S.-directed coup.