The opposition and the primary's winner Maria Corina Machado have insisted repeatedly it was transparent and fair.
The U.S. State Department is aware of the accusations and called for an investigation, a spokesperson said, adding the primary was "an important milestone" for Venezuela.
The investigation, requested by lawmaker Jose Brito, will center on accusations of electoral violations, financial crimes and conspiracy, Saab said during a press conference.
The electoral violations stem from the primary being organized without the National Electoral Council, Saab said.
Voter rolls for the primary included 2 million people who neither registered nor participated, Saab said, and financing for the primary has not been made public.
Persons:
Tarek Saab, Maria Corina Machado, Machado, Nicolas Maduro's, Nicolas Maduro, Jose Brito, Saab, Jesus Maria Casal, Mildred Camero, Roberto Abdul, Hadi, Vivian Sequera, Mayela Armas, Julia Symmes Cobb, Natalia Siniawski, Oliver Griffin, Helen Popper, Marguerita Choy, Rod Nickel
Organizations:
Venezuela's, Washington, U.S . State Department, Electoral Council, Saab, Voters, Thomson
Locations:
CARACAS, Washington, Maduro, Barbados, U.S, Venezuela, Sumate