A spokesman for the group said the offer, which is equivalent to 39 euros per share, is 13 per cent higher than Barclays' offer, to which ABN Amro has this week provisionally agreed.
The offer from the consortium, which includes Dutch-Belgian bank Fortis and Spanish bank Santander, is comprised of 70 per cent cash and a further 30 per cent in shares in Royal Bank of Scotland (RBS).
However, conditions stipulated by the offer include keeping La Salle Bank, which ABN Amro has recently announced it is looking to sell to Bank of America for $21 billion.
A statement from the consortium outlining why their counter bid represented a better prospect for the Dutch said: "The banks believe that execution risk would be lower than in a transaction with Barclays. The banks believe that the potential transaction will create stronger businesses with enhanced market positions and growth prospects in each of ABN Amro's main markets."