WASHINGTON, United States (AFP) — US President Donald Trump on Saturday threatened Venezuela with "incalculable" consequences if it refuses to take back migrants it has "forced into the United States," as tensions soar with Caracas.

"We want Venezuela to immediately accept all of the prisoners, and people from mental institutions... forced into the United States of America," Trump said. "Thousands of people have been badly hurt, and even killed, by these 'Monsters.'"

The president added, in all-caps: "Get them the hell out of our country, right now, or the price you pay will be incalculable!"

Venezuela on Friday accused the US of waging an "undeclared war" in the Caribbean and called for a United Nations probe of American strikes that have killed over a dozen alleged drug traffickers on boats in recent weeks.

Washington has also deployed warships to international waters off Venezuela's coast, backed by F-35 fighters sent to Puerto Rico in what it calls an anti-drug operation.

The biggest US naval deployment in the Caribbean in decades has stoked fears the US is planning to attack Venezuelan territory.

The strikes have prompted debate over the legality of the killings, with drug trafficking itself not a capital offense under US law.

Nor has Washington provided specific details to back up its claims that the boats targeted had actually been trafficking drugs.