(Reuters) - Activist investor Starboard Value LP asked office supplies retailer Staples Inc (>> Staples, Inc.) to "improve" the composition of its board to complete the acquisition of Office Depot Inc (>> Office Depot Inc) and fully integrate its smaller rival.

Starboard, which did not suggest any candidate for the board in a letter to Staples on Wednesday, said the combined company could be worth $32-$37 per share.

Staples shares were down 1 percent at $16.63 on the Nasdaq in early trading. Office Depot's shares were slightly down at $9.42.

The hedge fund's founder and Chief Executive Jeffrey Smith in January pushed Staples to merge with Office Depot, saying a combined company would lead to greater savings and help fend off competition from online rivals..

Staples was not immediately available for comment.

Starboard replaced Darden Restaurants Inc's (>> Darden Restaurants, Inc.) entire board with its 12-director slate last October, in a rare victory for dissident investors.

Staples, the No.1 U.S. office supplies retailer, agreed to buy No.2 Office Depot in a $6.3 billion deal announced a month ago. The deal is awaiting approval from the U.S. Federal Trade Commission, which it is widely expected to get.

The merger would also help the company better compete with big-box chains such as Wal-Mart Stores Inc (>> Wal-Mart Stores, Inc.) that sell the same core office supplies, such as paper and ink toner, for less.

Starboard holds a 4.5 percent stake in Staples and boosted its holdings in Office Depot to nearly 10 percent in December.

(Reporting by Sruthi Ramakrishnan in Bengaluru; Editing by Joyjeet Das and Sriraj Kalluvila)