US President Donald Trump warned on Saturday that the airspace above and near Venezuela should be considered closed, the latest escalation in a standoff with leftist leader Nicolas Maduro.

"To all Airlines, Pilots, Drug Dealers, and Human Traffickers," Trump wrote on his Truth Social network, "please consider THE AIRSPACE ABOVE AND SURROUNDING VENEZUELA TO BE CLOSED IN ITS ENTIRETY."

Caracas slammed the warning as a "colonialist threat" and called it the latest "extravagant, illegal and unjustified aggression against the Venezuelan people."

Trump's administration is piling pressure on Venezuela, with a major military deployment in the Caribbean and strikes against Venezuelan vessels in the Caribbean Sea and eastern Pacific Ocean since early September, killing at least 83 people.

Raising the stakes further, Trump warned earlier this week that efforts to halt Venezuelan drug trafficking "by land" would begin "very soon."

The tensions have now led to major disruptions in air travel to and from Venezuela.

US aviation authorities last week urged civilian aircraft operating in Venezuelan airspace to "exercise caution" due to the "worsening security situation and heightened military activity in or around Venezuela."

That warning prompted six airlines that account for much of the travel in South America to suspend flights to Venezuela.

The move infuriated Caracas and led it to ban the companies – Spain's Iberia, Portugal's TAP, Colombia's Avianca, Chile and Brazil's LATAM, Brazil's GOL and Turkish Airlines – for "joining the actions of state terrorism promoted by the United States government."

The New York Times reported on Friday that Trump and Maduro had spoken by phone last week and discussed a possible meeting in the United States, a day after the US president said efforts to halt Venezuelan drug trafficking by land were imminent. (AFP)