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.
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".