InBev NV will ask Anheuser-Busch Cos. shareholders to oust the American brewer’s board after the directors rejected InBev’s $46.3 billion hostile takeover offer because it was too low.

InBev is seeking to use a process outlined in Anheuser-Busch’s bylaws that allows shareholders to vote on a new board without a meeting, the Leuven, Belgium-based brewer said yesterday in an American regulatory filing. Anheuser-Busch called InBev’s maneuver “self-serving” and said it will ask shareholders to ignore it.

Anheuser-Busch, the maker of the 132-year-old Budweiser beer, rejected InBev’s offer of $65 a share on June 26, saying it undervalued the company. The Belgian brewer wants to replace the chief executive officer, August A. Busch IV, and other directors with a board that includes the CEO’s uncle and great-grandson of Anheuser-Busch’s founder, Adolphus A. Busch IV, who has urged acceptance of the bid.

“It’s getting less likely that InBev will increase its offer,” an analyst at KBC Securities in Brussels with an “accumulate” rating on the Belgian company, Wim Hoste, said by telephone. “This is a way of keeping up pressure. The board of Anheuser-Busch in its current form will start to talk to InBev in a more friendly way, or a renewed board could be more positive.”

The directors may be replaced with the permission of holders representing more than half the shares outstanding, InBev said. The brewer will wait for the Securities and Exchange Commission to review its proposal before asking shareholders to vote, an InBev outside spokeswoman, Nina Devlin of Brunswick Group LLC, said.