In response, US national security adviser John Bolton warned of "serious consequences for those who attempt to subvert democracy and harm Guaido", in a tweet that described Saab as the "illegitimate former Venezuelan Attorney General".
Venezuela has been embroiled in political power tug-of-war since opposition leader Juan Guaido declared himself interim president last week as part of a campaign to remove disputed President Nicolas Maduro.
The move comes after the United States earlier said it has handed control of Venezuela's U.S. bank accounts to Guaido, to prevent President Nicolas Maduro from commandeering them in an eventual exit from power.
"Russia is doing everything to support the lawful government of Maduro", he said, according to Russian news agency Interfax.
The Treasury secretary added that in the "short term" he expects "modest" impact on USA refineries. Its proceeds must instead be held in blocked US accounts, the Treasury said.
The latest United States sanctions announced on Monday appear to be aimed at pressuring President Nicolas Maduro to step down and to build on the momentum that has mounted in recent weeks against him at home and overseas.
Maduro said he wants peace, but also announced more military games for February.
The United States will issue temporary licenses to ensure US, Caribbean and European refineries that rely on Venezuelan crude can keep buying PDVSA oil but he said many had been taking steps to find other sources. "The oil belongs to the Venezuelan people, and therefore the money PDVSA earns from its export will now be returned to the people through their legitimate constitutional government".
The sanctions will not likely affect consumer prices at the gas pump but will hit oil refiners, particularly those on the U.S. Gulf Coast.
"I think, on the one hand, we've been able to cut off Venezuela oil going forward, but we're managing this with the USA refineries", he said.
The sanctions announced Monday also prohibit USA exports of diluent to Venezuela-a thinning agent that allows dense and viscous crude to flow through pipelines to be refined and sold.
The sanctions would be the latest move in Trump's campaign oust the leftist regime of Maduro, who succeeded the late President Hugo Chavez in 2013.
The sanctions threatened to hasten PDVSA's unraveling.
It added those shipments have fallen to about 505,000 barrels per day from over 900,000 bpd earlier this decade and Venezuela now supplies only 13 USA refiners, down from 22 seven years ago.
During the previous fiscal year, the USA imported roughly 505,300 barrels per day from Venezuela, about 6.4 percent of its total oil imports.
"We're also aware of significant contacts between general officers of the Venezuelan military and supporters of the National Assembly", Bolton added.
Washington has recognised Guaido as the South American country's acting president and says that strongman President Nicolas Maduro should leave power.