ABI has offered to pay £45 per share for SABMiller, up from £44 a share beforehand, valuing the Peroni brewer at £79bn rather than the previous £71bn.
It follows the slump in sterling to 31-year lows following the UK’s referendum vote to leave the EU last month.
In May, SABMiller also revealed a 16% fall in profits as costs rose ahead of the deal.
ABI increased the bid after SABMiller’s chairman talked to his ABI counterpart about the impact on the deal of currency and market movements.
But the pair did not discuss or agree ABI’s revised offer, which the latter said was final.
SABMiller’s sixth-biggest investor, Aberdeen Asset Management, said the revised offer undervalued the company and was unacceptable, according to Bloomberg.
Stella Artois brewer AB Inbev also makes Budweiser, Corona and Leffe, while Britain-based SABMiller - which holds second position - owns Peroni, Grolsch and Pilsner Urquell beers.
ABI employs about 1,000 people at its UK breweries in Magor, Samlesbury and Mortlake, as well as its company headquarters in Luton. It has at least 200 beer brands.
SABMiller has around 69,000 staff in more than 80 countries, from Australia, Zambia and Colombia to the Czech Republic, South Africa and the US, also producing more than 200 beers.
Formerly known as South African Breweries, SAB acquired US rival Miller Brewing Company in 2002, resulting in the renaming of the group as SABMiller.
A merged group would add AB InBev's dominance of Latin America to SABMiller's strong presence in Africa, as well as their breweries in Asia.