NEW YORK — Anheuser-Busch yesterday rejected a $65-per-share cash offer from Belgium-based brewer InBev.

A press release and three-page letter by chairman and CEO August Busch IV to InBev CEO Carlos Brito was the first public response to the $46 billion takeover proposal made on June 11.

In the letter, Busch, a member of the founding family who became president and CEO in 2006, says that the board "unanimously concluded your proposal is inadequate and not in the best interests of Anheuser-Busch shareholders." The letter says the board "carefully and thoroughly examined all aspects of your proposal with the assistance of independent advisers."

InBev has stated publicly that it stands by its $65-per-share offer. A-B, whose stock prices had been flat for about five years, saw its stock rise 65 cents to $62 in after-hours trading yesterday.

"This is turning into a nice barroom brawl," said Juli Niemann, analyst at Smith Moore in St. Louis. "Clearly, they are gunning for a higher cash price, and $65 is a really, really good price. It's also a face-saving thing, as well. You won't see $65 a share in my lifetime, even with a restructuring by A-B."

Niemann said there's a chance that InBev could sweeten its offer with InBev stock, which has been a "good performer."

InBev has grown through acquisitions and has generated shareholder value through sharp cost-cutting measures. Brito has aggressively pursued Anheuser-Busch publicly with three letters and lengthy videos citing promises to keep open A-B's 12 U.S. breweries, retain Budweiser's global headquarters in St. Louis and incorporate the heritage of Anheuser-Busch into the name of the combined entity.

Yesterday, Brito notified A-B that it had sought a ruling in Chancery Court in Delaware, where A-B is incorporated, to see if it could seek shareholder approval to remove without cause A-B's 13 board members. Eight board members are subject to removal without cause under A-B's charter and Delaware law, but five others can be removed only through written consent by shareholders.

Busch's letter did not address yesterday's filing but does say that InBev's "suggested synergies" are instead "profit enhancements" that "we can deliver independent of a transaction."

A-B will address restructuring plans this morning on an investor call. Beer remains the company's biggest business, with U.S. beer sales reaching $12.1 billion and global beer sales topping $1 billion.