AB InBev on Wednesday raised its offer for SAB to £42.15 a share, having previously bid £38 and £40.
SABMiller closed up 2.4% at £37.08, having risen sharply since InBev first made its move last month.
Any deal between the two would create the world's biggest brewer, worth more than £180bn.
SABMiller said its board had formally considered the new offer, and had "unanimously rejected the proposal as it still very substantially undervalues SABMiller, its unique and unmatched footprint, and its standalone prospects".
AB InBev brews Budweiser, Stella Artois and Corona, while SAB brews Peroni and Grolsch, among others.
If a deal does go through, the merged company would produce one-third of the world's beer.
On Tuesday, SAB reported a 9% fall in revenues for the three months to September, which it blamed on weakening emerging market currencies.
Sales volumes were up 2%.
Shares in AB InBev closed up 0.6% in Brussels at €98.65.
SABMiller has rejected an improved offer from Anheuser-Busch InBev that it says "very substantially undervalues" the company.