The move comes after the US recognised interim president Juan Guaido, who declared himself interim president on Wednesday, saying the constitution gave him powers to form a transitional government until new elections.
The US quickly fell in behind him, a move that prompted anger from Mr Maduro, who threatened to expel US diplomats from the country. In return the US State Department said Mr Maduro no longer had the right to do that and that it would now conduct relations via Mr Guaido.
Speaking on Thursday, national security adviser John Bolton said the US would cut the flow of money to Mr Maduro and instead ensure oil revenue went to Mr Guaido. In a country which is one of the world’s largest oil exporters, such a move would significantly strengthen Mr Guaido.
Mr Bolton said: “What we’re focusing on today is disconnecting the illegitimate Maduro regime from the sources of his revenues.
“We think consistent with our recognition of Juan Guaido as the constitutional interim president of Venezuela that those revenues should go to the legitimate government.”
Mr Bolton added that the process was “very complicated” and that officials were still deciding how this would work.
Mr Guaido, 35, the new leader of the assembly, announced his dramatic move to cheering supporters in the capital, Caracas – two weeks after Mr Maduro was sworn in for a controversial second term.
Britain, Germany, France, Argentina, Brazil, Canada, Colombia and Chile are among the countries that have also backed him, while Mexico, Bolivia and Turkey have sided with Mr Maduro.
Protesters clashed with security forces on Wednesday night in the capital of Caracas and 14 people were killed.
Mr Guaido told broadcaster Univision on Thursday that this was “the beginning of the end” for Mr Maduro, vowing to guarantee humanitarian aid and bring in new economic measures.
“Our challenge is to secure free elections, and we want them as soon as possible. But we are living in a dictatorship.”
The need among Venezuelans is desperate – millions have fled the country in recent years due to massive inflation and a shortage of food and medicine. Inflation in Venezuela is predicted to hit 10,000,000% this year, according to the International Monetary Fund.
My Maduro has retained power mainly thanks to military support and the election that gave him another term was boycotted by opposition parties and described as fraudulent by the US and European Union. Nicolás Maduro supporters say this latest challenge to his power is part of a US-led conspiracy.