Donald Trump's threat of US military strikes against drug cartels inside Mexico is a non-starter, Mexican President Claudia Sheinbaum said Tuesday.

'It's not going to happen,' she said at a press conference, responding to Trump's warning that he would do 'whatever we have to do,' including strikes within the territory.

Trump on Monday told reporters in the Oval Office that he would be 'OK' with assaults on drug lords operating inside Mexico, arguing that it would be justified to stop the inflow of the deadly opioid fentanyl. 

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'Would I launch strikes in Mexico to stop drugs? It's OK with me. Whatever we have to do to stop drugs,' Trump said.

'I didn't say I'm doing it, but I'd be proud to do it. Because we're going to save millions of lives by doing it.'

The questions about Mexico come after Trump mobilized the largest US fighting force in the Caribbean since the Cold War to target gangsters coming from Venezuela.

Since September, US forces have killed at least 83 people via air strikes on boats accused of ferrying drugs in international waters.

The United States has released no details to back up its claims that the people targeted in both the Caribbean and eastern Pacific in the more than 20 strikes were actually traffickers.

Mexico's President Claudia Sheinbaum speaks during her daily press conference at Palacio Nacional in Mexico City on Monday

Mexico's President Claudia Sheinbaum speaks during her daily press conference at Palacio Nacional in Mexico City on Monday

A Mexican cop patrols beside burned out cars after an attack by cartel thugs on a highway near Quiroga, Michoacan state, Mexico on Monday

A Mexican cop patrols beside burned out cars after an attack by cartel thugs on a highway near Quiroga, Michoacan state, Mexico on Monday

Trump told reporters he would not rule out troops on the ground in Venezuela, but added that he planned to talk with the country's socialist dictator Nicolas Maduro.

Asked if he would rule out a ground invasion, Trump replied: 'No, I don't rule out that, I don't rule out anything. 

'At a certain period of time, I'll be talking to [Maduro],' he added, while insisting that the tyrant 'has not been good to the United States.' 

'We just have to take care of Venezuela,' Trump said. 'They dumped hundreds of thousands of people into our country from prisons.' 

Hours later, Maduro said on his weekly television show that he was ready to talk 'face to face' with anyone in the United States 'who wants to talk to Venezuela.'

A contingent of US Marines is currently conducting military exercises in Trinidad and Tobago, the second such maneuvers in less than a month between Washington and the small English-speaking archipelago located about six miles from Venezuela.

But Trinidad and Tobago's leader said Monday that he would not allow the island to be used as a launching platform for an attack, nor was it ever asked to.

'The US has NEVER requested use of our territory to launch any attacks against the people of Venezuela,' said Prime Minister Kamla Persad-Bissessar, a close Trump ally.

Trump with Gianni Infantino, the FIFA boss, and Macro Rubio, in the Oval Office on Monday

Trump with Gianni Infantino, the FIFA boss, and Macro Rubio, in the Oval Office on Monday

'Trinidad and Tobago will not participate in any act that could harm the Venezuelan people,' she added, emphasizing that Washington and Caracas should resolve their differences through dialogue.

Venezuela has accused Washington of seeking regime change in Caracas with its military build-up including an aircraft carrier group, warships and several stealth jets.

Washington accuses Maduro of leading a 'terrorist' drug cartel, a charge he denies.