Venezuelan President Nicolas Maduro offered to engage in direct talks with the administration of US President Donald Trump days after the first US strike on a boat from the South American country that Trump says was carrying drug traffickers.

In a letter to Trump that was published by Venezuela on Sunday, Maduro rejected US claims that Venezuela played a big role in drug trafficking, noting that just 5 percent of drugs produced in Colombia are shipped through Venezuela – of which he said 70 percent were neutralised and destroyed by Venezuelan authorities.

"President, I hope that together we can defeat the falsehoods that have sullied our relationship, which must be historic and peaceful," Maduro wrote in the letter.

"These and other issues will always be open for a direct and frank conversation with your special envoy (Richard Grenell) to overcome media noise and fake news."

He noted that Grenell had helped quickly resolve earlier allegations that Venezuela was refusing to take back migrants, adding, "To date, this channel has functioned flawlessly."

Twice-weekly deportation flights moving illegal migrants to Venezuela from the US have continued uninterrupted despite the US strikes, sources familiar with the matter told Reuters.

Maduro's letter was dated September 6, four days after a US strike on a vessel that the Trump administration has claimed, without evidence, was carrying drug traffickers.

The strike killed 11 people who Trump said were members of the Tren de Aragua gang and engaged in drug trafficking.

After publishing the letter on Sunday, the Venezuelan government confirmed it was given to an intermediary on September 6.

The White House had no immediate comment.

Trump doubled down on his pressure campaign on Saturday, warning in a post on his Truth Social platform that Venezuela must accept the return of all prisoners whom he said Venezuela had forced into the US, or else pay an "incalculable" price.

Trump on Friday announced at least the third strike against alleged drug vessels from Venezuela amid a large US military buildup in the southern Caribbean that includes seven warships, a nuclear-powered submarine and F-35 stealth fighters.

The strike killed "3 male narcoterrorists aboard the vessel," Trump said, without providing evidence.

The Venezuelan government, which says it has deployed tens of thousands of troops to fight drug trafficking and defend the country, has said none of the people killed in the first strike belonged to Tren de Aragua.

It also denies accusations of links between high-ranking Venezuelan authorities and drug gangs.

Maduro has repeatedly alleged the US is hoping to drive him from power. Trump this week denied he was interested in regime change, but Washington last month doubled its reward for information leading to Maduro's arrest to US$50 million, accusing him of links to drug trafficking and criminal groups.

Maduro reiterated his denial in his letter to Trump.

"This is the most egregious instance of disinformation against our nation, intended to justify an escalation to armed conflict that would inflict catastrophic damage across the entire continent," he wrote in his letter to Trump. (Reuters)