On Monday the Wall Street Journal reported he was being investigated by the US for possible drug-trafficking and money-laundering.
Mr Cabello dismissed the accusations, saying no proof had been offered.
In March the US imposed sanctions on a group of Venezuelan officials.
Venezuelan opposition leaders and US officials have previously made similar accusations against the governments of President Nicolas Maduro and his predecessor Hugo Chavez.
Mr Cabello is both president of the National Assembly and the second most senior official in the governing Socialist Party.
Last month he filed a defamation suit against 22 people linked to various media outlets who had republished details of the US accusations.
Correspondents say he sees the accusations as part of a campaign to discredit the country's socialist achievements and to destabilise it months before a parliamentary election.
The US has sanctioned at least 50 Venezuelan government officials whom it accuses of drug-trafficking and human rights abuses.
In December, President Barack Obama signed a decree classifying Venezuela as a "security threat".
Last month the 11 members of the Alba group of Latin America countries urged him to repeal the decree and made clear they backed Venezuela.
Thousands of Venezuelans marched through the streets in December in protest against the US sanctions against Venezuelan officials.

A planned December bout fell through because the fighters "ran out of time", said Klitschko's manager Bernd Boente.
"That'll be the biggest heavyweight fight for years," former world champion Klitschko, 40, told German newspaper Bild.
The WBA has yet to state whether its vacant title would be on the line.
Promotor Eddie Hearn initially blamed confusion over the titles on offer and a "minor injury" to Ukrainian Klitschko for the failure to arrange a December date.
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Klitschko, who will turn 41 in March, lost his WBA WBO and IBF belts to Tyson Fury in November 2015.
Two attempts to stage a rematch collapsed because the Briton suffered an ankle injury and was then declared "medically unfit". Fury has since vacated his WBO and WBA titles.
Joshua won the IBF belt with victory over Charles Martin in April.
"I want to box in March or April against IBF world champion Anthony Joshua," said Klitschko.
"I've never thought about stopping, not once, after the defeat and losing my belts.
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"As long as I can perform in the ring, am fit and motivated, I'll keep going. There will be a couple of big, spectacular fights with me in the ring."
Joshua, 27, has won all of his 17 fights since turning professional following his gold medal at the London 2012 Olympics.
He is expected to find an alternative opponent for his 10 December fight at Manchester Arena.
Former British champion David Price tweeted that he is "coming to knock you out", while American Eric Molina has also reportedly been contacted about a bout.
Venezuela's parliament has passed a motion defending its president, Diosdado Cabello, against what it described as "a campaign of lies by national and international media".
[NEXT_CONCEPT]
Wladimir Klitschko says he wants to fight British heavyweight world champion Anthony Joshua in "March or April".