Allergan Inc. has repeatedly rejected the offers as underpriced and risky. But Pearson said that Valeant believes an Allergan shareholder vote would "be overwhelmingly in support of the deal."
Valeant and Pershing—which has a 9.7 percent stake in Allergan—have continued to pursue Allergan despite the Irvine, California company's disinterest. The latest offer was worth about $53 billion. Allergan's market capitalization was about $47.5 billion in Tuesday morning trading.
Ackman previously said he would move to replace most of Allergan's board of directors as part of the battle for control of the company. Pearson said Tuesday that Pershing is looking to call a special shareholders meeting to remove six of Allergan's nine board members. Last week Pershing filed a lawsuit to confirm that its push for the special meeting won't trigger a defensive "poison pill" from Allergan.
Read MoreAllergan board says Valeant bid undervalues company
Allergan adopted a one-year shareholder rights plan after Valeant and Pershing announced their bid in April. Under the plan, if any person or group acquires a 10 percent or greater stake in the company, other stock owners would be allowed to acquire additional shares at a discounted rate.
Pearson said that a special meeting of Allergan shareholders could be held in August, but should take place by year's end.
An e-mail to Allergan for comment was not immediately returned.
Allergan's stock added 29 cents to $159.66 in morning trading Tuesday (click here for the latest quote), while shares of Valeant fell 47 cents to $117.28 (click here for the latest Valeant quote).
—By The Associated Press