U.S. Secretary of State Mike Pompeo speaks during a press briefing in Washington D.C., the United States, April 22, 2019. (Xinhua/Liu Jie)

WASHINGTON, May 1 (Xinhua) -- U.S. Secretary of State Mike Pompeo said on Wednesday that the United States will continue to raise cost for Cuba and Russia over their behaviors on Venezuela-related issue.

In an interview with Fox Business Network, Pompeo said that "you've seen the work that we've done already to raise the cost for the Cubans. We've taken a handful of actions. There are more that we will continue to work on. We'll do the same for the Russians."

"As the President said, they've got to go, and the Russians need to have the cost for that raised," Pompeo said.

He added that regarding sanctions and restrictions to Cuba, "there's certainly more to follow."

Pompeo's remarks came after U.S. President Donald Trump threatened on Twitter on Tuesday that if Cuban troops and militia do not cease their operations in support of Venezuela immediately, Cuba would suffer "a full and complete embargo" as well as "highest-level sanctions."

When asked about the possibility of U.S. military intervention in Venezuela, Pompeo insisted in Wednesday's interview that "military action is possible. If that's what's required, that's what the United States will do."

Washington has repeatedly alleged that Havana has thousands of intelligence and security forces in Venezuela to shore up the government of President Nicolas Maduro, which Washington is openly seeking to oust from power.

Cuban Foreign Minister Bruno Rodriguez responded to Trump's tweets also via Twitter, saying "there are no Cuban troops in Venezuela; nor are there any Cubans taking part in military or security operations there."

Noting that Cuba had only sent medical staff to Venezuela for humanitarian missions, Rodriguez said "I strongly reject Trump's total blockade threat."

U.S.-Cuba ties have deteriorated under Trump, who has rolled back the detente initiated by his predecessor, Barack Obama. The White House earlier announced a cap on remittances to Cuba and restrictions on non-family-related travels, a move that could affect American cruise companies and airlines that sail or fly to the island.