ABN's chief executive, Rijkman Groenink, told shareholders the offer was unacceptable on Thursday.
"The offer of Barclays is too low. We cannot ask shareholders to pay the difference from the consortium's bid," he told shareholders at a meeting to discuss the deal.
Reuters reported that the Dutch bank had called an 'extraordinary' meeting with shareholders to discuss the two offers for the company.
The RBS led consortium, which includes Belgian-Dutch group Fortis and Spain's Santander, have made mostly a cash bid, currently valued at $98 billion.
Barclays cash and share offer, is worth about $82.8 billion.