It would be "a very bad day" for Venezuela if it were to attack its neighbour Guyana or US-based energy giant ExxonMobil, US Secretary of State Marco Rubio has said during a visit to Guyana's capital.

Guyana and Venezuela are locked in a long-running dispute about which country has rights over the 160,000-square-km Esequibo area, which is the subject of an ongoing case at the International Court of Justice.

Washington has offered military support to the tiny South American country amid the territorial dispute and increasing US sanctions on Venezuela.

The US Navy cruiser Normandy and the Guyana Defence Force patrol vessel Shahoud were conducting exercises in international waters and the Guyana Exclusive Economic Zone, the US embassy in Guyana said in a social media post early on Thursday.

Tensions rose early this month when Guyana said a Venezuela coast guard patrol entered its waters and approached an output vessel in an offshore oil block operated by Exxon.

A consortium by Exxon, Hess and China's CNOOC controls all oil and gas output in Guyana, which this year is producing some 650,000 barrels per day.

The northwest portion of the block, close to Venezuela, has remained in force majeure as the Exxon group has been unable to complete exploration there.

Venezuela's communications ministry did not immediately respond to a request for comment.

Venezuela has previously said the vessel did not enter Guyanese waters as the maritime zone delimitation is still pending as part of the territorial dispute.

Guyana says Rubio promised protection against Venezuela

Rubio also described some Tren de Aragua gang members as being worse than Al Qaeda, while promising to double down on controversial forced deportations.

With Donald Trump's administration facing fierce criticism for deporting planes full of migrants from the United States without normal due process, Rubio defended the policy.

"These are some really bad people" Rubio said. "Tren de Aragua is one of the most dangerous gangs the world has ever seen," he said, referring to a group that has grown from Venezuelan prisons to become a thousands-strong transnational crime syndicate.

Also on Thursday, Guyanese President Irfaan Ali said Rubio promised US support for his oil-rich South American nation's sovereignty in the face of threats from Venezuela.

"I'm very pleased at the reassurance of the US, ensuring the safeguard of our territorial integrity and sovereignty," Ali told a joint news conference, saying that the two discussed Venezuela.