Aberdeen said the revised offer of 45 pounds ($59.14) a share, up from 44 pounds a share previously, undervalued the company and continued to favor SABMiller's two major shareholders, Altria and Bevco.
"We have engaged with SABMiller's Board on the differential treatment of shareholders since the deal was first constructed. The way that the value of the partial share offer has diverged from the cash offer has compounded our discomfort," it said.
Altria and Bevco should not be able to vote on the cash offer as they were inherently conflicted by their future stakes in AB InBev if the deal completes, it said.
"We believe the board's only choice is to treat Altria and Bevco as a separate class of shareholders and would urge them to make a public statement to this effect."
Failing a new offer, Aberdeen would "happily" remain a long-term shareholder in SABMiller, it added.