"The United States Guard is in active pursuit of a sanctioned dark fleet vessel that is part of Venezuela's illegal sanctions evasion," a US official said.
"It is flying a false flag and under a judicial seizure order."
Another official said the tanker was under sanctions but added that it had not been boarded so far and that interceptions can take different forms -including sailing or flying close to vessels of concern.
The officials, who were speaking on the condition of anonymity, did not give a specific location for the operation or name the vessel being pursued.
The White House did not immediately respond to a request for comment on Sunday.
US President Donald Trump last week announced a "blockade" of all oil tankers under sanctions entering and leaving Venezuela.
Trump's pressure campaign on Venezuelan President Nicolas Maduro has included a ramped-up military presence in the region and more than two dozen military strikes on alleged drug-trafficking vessels in the Pacific Ocean and Caribbean Sea near the South American country.
At least 100 people have been killed in the attacks.
The first two oil tankers seized were operating on the black market and providing oil to countries under sanctions, Kevin Hassett, director of the White House's National Economic Council, said in a TV interview on Sunday.
"And so I don't think that people need to be worried here in the US that the prices are going to go up because of these seizures of these ships," Hassett told CBS.
"There's just a couple of them, and they were black market ships."
But one oil trader told Reuters that the seizures may push oil prices slightly higher when Asian trading resumes on Monday.
"We might see prices increasing modestly at the opening, considering market participants could see this as an escalation with more Venezuelan barrels at risk," UBS analyst Giovanni Staunovo said.
Another analyst said the seizures raise geopolitical risks and are likely to raise friction in the shadow fleet of vessels that move oil from sanctioned countries like Venezuela, Russia and Iran.
The seizures could legitimise and encourage Ukraine to continue attacking Russian vessels and possibly encourage European countries to detain Russian-linked dark fleet vessels as well, said Matias Togni, oil shipping analyst at NextBarrel.
Venezuelan and Iranian oil output is already showing signs of slowing, Togni said, adding that he expects the same to happen with Russia.
Oil from countries under sanctions is likely to be offered at steeper discounts as logistics become more expensive, which could help cap the gains in benchmark oil prices, he said.
