Adds comment from Prologis from paragraph 2, details and background throughout

June 24 (Reuters) - Prologis PLD.N said on Wednesday warehouse landlord Segro SGRO.L rejected its £12.6 billion ($16.62 billion) all-share takeover proposal and urged shareholders to press the British firm's board to engage with the U.S. logistics firm.

Prologis argued the FTSE 100 firm has traded at a persistent discount to its net asset value and faces structural constraints including balance sheet limitations that prevent it from unlocking value in its development and artificial intelligence data center pipeline.

"Prologis urges Segro shareholders to encourage the Segro board to engage with Prologis to allow a binding offer to be put to Segro shareholders for their consideration," Prologis said in a statement.

Segro could not be immediately reached for comment.

Under the terms of the proposed combination, Segro shareholders would have received 0.084 new Prologis shares for each share they held, implying a value of 925 pence apiece - a 24.7% premium to Segro's closing price on Tuesday.

The approach marks the latest attempt by a U.S. firm to snap up a London-listed company as weaker British valuations continue to attract American buyers with deeper pockets.

The company has until July 22 to unveil a firm offer for Segro or walk away, under British takeover rules.

($1 = 0.7580 pounds)