The US has instructed oil trading houses and refiners around the world to further cut dealings with Venezuela or face embargoes, even if the trades are not prohibited by published US sanctions.
The demand comes as Washington's attempts to remove Venezuelan President Nicolas Maduro and install opposition leader Juan Guaido have stalled.
The US call is further evidence of how it is leaning on non-US companies to achieve its foreign policy goals.
Washington imposed new sanctions on Venezuela's oil industry this year but some companies have continued to supply the country with fuel from India, Russia and Europe.
The White House is particularly keen to end deliveries of petrol and refined products used to dilute Venezuela's heavy crude oil to make it suitable for export.
Jet fuel and diesel would be exempt for humanitarian reasons, sources said.
The US Treasury's office of foreign assets control announced a ban in early February on the use of its financial system in oil deals with Venezuela after April.
But as recently as this week, the US State Department called on foreign companies to say that the scope of the sanctions is wider.
Sources said the State Department made it clear that any kind of oil trade, whether it be direct, indirect or barter, would be considered a breach.
"We continue to engage with companies in the energy sector on the possible risks they face by conducting business with PDVSA [Venezuela's state-owned oil company]," a spokesman for the State Department said.
"This is how the United States operates these days. They have written rules and then they call you to explain that there are also unwritten rules that they want you to follow," a source said.
Washington has increasingly been using its oil influence. At a major oil event in Houston this month, Secretary of State Mike Pompeo made a rare appearance and laid out a vision of working with energy companies to isolate Iran and Venezuela.
Venezuela's overall exports of crude and fuel dropped to 920,000 barrels per day in the first month of sanctions, from more than 1.5 million bpd in the three months before, Refinitiv Eikon and PDVSA data show.
But Russia remains a staunch supporter of Mr Maduro's government, which has plunged Venezuela into an economic and humanitarian crisis.
In an increase in tension, President Donald Trump called on Moscow to remove all of its soldiers from Venezuela after a Russian military contingent arrived just outside of Caracas.
Mr Trump said "all options" were open to make that happen.
Russia responded on Thursday saying it had sent specialists to Venezuela under a military co-operation deal.
The biggest trading companies based in Europe, such as Vitol, Gunvor, Mercuria, Trafigura and Glencore, account for about 10 per cent of global oil trade.