BRUSSELS, Belgium — Beer giant Anheuser-Busch InBev has offered to buy fellow brewing behemoth SABMiller plc for $104 billion (U.S.) but saw its increased bid quickly rejected.

AB InBev said Wednesday that it’s now offering £42.15 ($64.60) per share for SABMiller, a 44% premium from the latter’s closing share price of £29.34 ($44.97) on Sept. 14, the last business day before renewed speculation that AB InBev approached SABMiller about a merger. Recently, AB InBev made two written proposals in private to SABMiller, one for £38.00 per share ($58.24) and then another for £40.00 per share ($61.31).

SABMiller’s board unanimously rejected AB InBev’s new offer for the company. As with the earlier acquisition proposals, SABMiller said Wednesday that AB InBev’s latest bid greatly undervalues the company.

“SABMiller is the crown jewel of the global brewing industry, uniquely positioned to continue to generate decades of stand-alone future volume and value growth for all SABMiller shareholders from highly attractive markets,” SABMiller chairman Jan du Plessis said in a statement. “AB InBev needs SABMiller but has made opportunistic and highly conditional proposals, elements of which have been deliberately designed to be unattractive to many of our shareholders. AB InBev is very substantially undervaluing SABMiller.”

Both companies already dominate the global beer market. But AB InBev said Wednesday that an AB InBev-SABMiller combination would create “a truly global brewer” with operations in virtually every major beer market, including key emerging regions with strong growth prospects such as Africa, Asia, and Central and South America. The merged entity would generate sales of about $64 billion, according to AB InBev.

“We have the highest respect for SABMiller, its employees and its leadership and believe that a combination of our two great companies would build the first truly global beer company,” AB InBev chief executive officer Carlos Brito stated Wednesday. “Both companies have deep roots in some of the most historic beer cultures around the world and share a strong passion for brewing as well as a deep seated tradition of quality. By bringing together our rich heritage, brands and people we would provide more opportunities for consumers to taste and enjoy the world’s best beers. We also both strive to have a positive impact on the communities in which we work and live as two of the world’s leading corporate citizens. Put simply, we believe we can achieve more together than each of us could separately, bringing more beers to more people and enhancing value for all of our stakeholders.”

Around mid-September, the two companies confirmed that AB InBev was making overtures to SABMiller about a merger. SABMiller’s board declined two proposals later that month. AB InBev said Wednesday that it’s “disappointed that the board of SABMiller has rejected both of these prior approaches without any meaningful engagement.”