BOSTON, Nov 7 (Reuters) - Valeant Pharmaceuticals International Inc can pay "substantially" more for Allergan Inc and should get a fair shot at buying it, William Ackman, the Botox maker's biggest shareholder, said on Friday.

Ackman said this in a letter to Allergan's board the day after the company said it was discussing a merger with another company, widely reported to be Actavis, to fend off hostile bidder Valeant.

Ackman, whose hedge fund Pershing Square Capital Management owns nearly 10 percent of Allergan, asked the board to see which suitor comes up with the best offer.

He urged the board to run an auction "where neither party is the favored bidder, and both are encouraged to offer maximum value - before any obligation to pay a breakup fee is incurred."

Valeant shares fell nearly 1 percent in early trading on Friday amid talk that the company's proposed plan to buy Allergan might collapse. Allergan stock was down 1.6 percent.

Valeant and Ackman shocked Wall Street in April when they said they were working on a takeover deal that Allergan has steadfastly rebuffed as it tries to find another merger partner.

Neither Allergan nor Valeant had any immediate comment on Ackman's letter.

Ackman wants to replace most of the board next month at a special shareholder meeting and has written to the directors before, telling them to take their fiduciary duties more seriously.

(Reporting by Svea Herbst-Bayliss, Rod Nickel and Caroline Humer; Editing by Lisa Von Ahn)