Trump made the remarks while video conferencing with deployed US troops to mark the Thanksgiving holiday.
Several of the US military groups that Trump addressed were actively participating in his anti-drug operation, dubbed "Southern Spear," which has seen a large military buildup in the Caribbean.
Addressing a Texas-based Air Force bombing unit, Trump, reading from prepared remarks, said: "In recent weeks, you've been working to deter Venezuelan drug traffickers, of which there are many."
It was not immediately clear what actions Trump was specifically referencing.
The US military has carried out a series of airstrikes against boats it claims were trafficking drugs in international waters, without offering evidence to back up its claims.
Those strikes in the Caribbean and eastern Pacific have killed at least 83 people, according to an AFP tally of publicly released figures.
Washington has also carried out multiple shows of aerial force in the region in recent weeks, with B-52 and B-1B bombers flying near Venezuela's coast.
Elaborating on US efforts to halt drug trafficking, Trump said: "We've almost stopped -- it's about 85 percent stopped by sea."
"You probably noticed that people aren't wanting to be delivering by sea, and we'll be starting to stop them by land," he said.
"Also the land is easier, but that's going to start very soon," he added.
- Ratcheting pressure -
The remarks come as Trump's administration continues to pile pressure on Venezuela, despite the US president saying in recent days that he was open to dialogue with Venezuelan leader Nicolas Maduro.
With an aircraft carrier group and numerous other assets in the Caribbean, Washington on Monday designated an alleged Venezuelan drug cartel a foreign terrorist organization, while top US military officials also traveled to the region this week.
Defense Secretary Pete Hegseth and his wife spent the Thanksgiving holiday on Thursday with troops aboard the aircraft carrier.
The Pentagon released a video showing him serving up turkey dinners in the mess and expressing gratitude to the troops for "interdicting cartels" and "defending the American people."
A day earlier, the Dominican Republic, a US ally in the Caribbean, told Hegseth that Washington could use an air base and an airport for its counter-narcotics operations.
- Air disruptions -
Leftist Maduro, whose re-election last year was widely rejected by the international community as fraudulent, believes the operation is secretly aimed at overthrowing him.
He has reacted defiantly, staging military exercises and mass rallies aimed at projecting strength and popular support.
The tensions have now led to major disruptions in air travel to and from Venezuela.
Last week, six airlines that account for much of the air travel in South America suspended flights to Venezuela following safety warnings from the US Federal Aviation Administration (FAA).
The FAA cited the "worsening security situation and heightened military activity in or around Venezuela."
In response, Venezuela's aviation authority said Wednesday that it had banned the airlines -- 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."
Portuguese Foreign Minister Paulo Rangel accused Venezuela of a "disproportionate" reaction.
Portugal has "no intention of canceling our routes to Venezuela, and that, obviously, we only did so for security reasons," he said.
A source from Iberia told AFP that the company hoped to resume flights to Venezuela "as soon as possible, as soon as full security conditions are met."
It added that the Spanish airline "cannot operate in areas where there is a high security risk" and added that Spain's aviation authority had recommended not flying at this time to Venezuela.
The flight suspension has so far affected more than 8,000 passengers on at least 40 different flights, according to the Venezuelan Association of Travel and Tourism Agencies.
A small number of Venezuelan companies, including Avior and Laser, continue to offer a limited number of flights to Spain and regional cities.
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