The consortium's $53.01 (38.40 euros) per share offer for ABN Amro will last until October 5, becoming unconditional if more than 80% of ABN Amro shareholders tender their shares.
ABN Amro shares closed down 1.1% at $50.58 (36.63 euros) in Amsterdam, suggesting investors were not fully convinced RBS would win the bidding war.
Barclays has proposed an all-share bid worth $46.74 (33.86 euros) per ABN Amro share based on the British bank's closing price Friday -- around 10% less than the RBS bid.
But Barclays has suggested it may try to sweeten its offer or add a cash element to improve its attractiveness to shareholders. Barclays has until August 6 to file its offer.
Analysts say that, based on price alone, Barclays cannot hope to win a battle with RBS and its partners, Fortis of Belgium and Banco Santander Central Hispano .
Fortis wants ABN Amro's Dutch operations, Santander wants its Brazilian and Italian arms, and RBS wants the rest, including its investment banking arm.
Barclays Chief Executive John Varley has said that, while his bank's bid may be lower, it would offer a better long-term return to shareholders and avoid what he called the planned carve up of the company by the consortium.
A potential hurdle remaining for RBS is that Fortis' shareholders must vote on a proposed $18 billion (13 billion euros) share issue it needs to finance its part of the deal -- that's about a third of the Belgian bank's size by market capitalization.
Fortis shareholders meet on Aug. 6, earlier the same day Barclays' bid is due.