Herbalife Ltd. on Thursday said that it would postpone next month’s annual shareholder meeting for five days so it can continue discussions with Carl Icahn about adding more of his nominees to the company’s board.

Icahn is one of the largest shareholders and most vigorous public supporters of the embattled downtown L.A. supplement company. Herbalife has been under attack by another New York activist investor, Bill Ackman.

Herbalife yesterday said the Federal Trade Commission had launched an inquiry into the company’s operations. Ackman has been lobbying regulators to investigate the company, characterizing its multilevel marketing sales model as an illegal Ponzi scheme.

Herbalife has not yet filed its proxy statement for the meeting with the Securities and Exchange Commission. The annual meeting, which had been scheduled for April 24, was rescheduled to April 29. It is still set to take place at the company’s corporate headquarters in the L.A. Live complex.

Herbalife shares on Thursday closed down $3.26, or 5 percent, to $7.31 on the New York Stock Exchange. They had fallen more than 7 percent on Wednesday following news of the FTC inquiry.