In a securities filing, GPA said the offer does not serve the best interests of the firm and its shareholders, as the price offered falls short of "financial reasonableness for a transaction aiming at a controlling interest."
The Brazilian retailer also said that the proposal presented by Gilinski does not provide sufficient elements to assure the board of its binding nature or a "reasonable expectation of concluding a transaction."
Last month, GPA declined Gilinski's offer to pay $836 million (€750.5 million) for nearly 97% of Éxito.
Éxito, which operates South American supermarkets and shopping malls, has a market value of some $1.3 billion (€1.17 billion), according to Refinitiv data.
In January, GPA said it has taken the first steps towards spinning off Éxito and plans to distribute its shares to existing shareholders.
Reuters reported last year that GPA was considering the spin-off, as its French parent company Casino planned to simplify its structure in Latin America to reduce its debt.
In a securities filing, GPA said Exito had applied to be a publicly-held company in Brazil and list Brazilian Depositary Receipts (BDRs) on the Sao Paulo stock exchange. Exito also plans to list American Depositary Receipts (ADRs) in New York. [Additional reporting by ESM]