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.

The 21-year-old, who has appeared 82 times for Brighton, played five games on loan at Karl Robinson's Championship strugglers earlier this campaign.
The England Under-21 international is eligible for Saturday's FA Cup third-round match against Northampton Town.
"I've been here before, I know what the club is all about and I just can't wait to get started," he said.
Robinson added to the club website: "I felt he was a real success in his first spell with us earlier this season and this was highlighted when we looked back and saw he was the top of our attacking stats for a midfield player.
"When he was here before, Darren Potter wasn't fit and Samir Carruthers wasn't playing in central midfield and, as a group, this time around I'm sure they will offer good balance."
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Sean Corrigan, 31, was found at a flat in St Mary's Garden and later died in hospital.
Post mortem results indicated he may have died in suspicious circumstances.
Det Ch Insp Justyn Galloway said police believe Mr Corrigan may have been assaulted in the hours prior to his death.
"We are carrying out a full investigation into Sean's death," he said.
"We have examined CCTV footage and spoken to a number of witnesses. We will also be carrying out house to house enquiries in the area over the coming days.
"It is vital that we speak to anyone who may have more information in relation to Sean's movements that night and what happened in the apartment.
"I would urge the local community to help us ascertain what happened to Sean by coming forward with information. If you were in the area between 1am and lunchtime, if you saw any suspicious activity or if you have any other information about Sean's death which might assist us with our enquiries, then please get in touch."
SABMiller has rejected an improved offer from Anheuser-Busch InBev that it says "very substantially undervalues" the company.
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