Pebblebrook said its latest offer for LaSalle represented an implied price of $37.80 per share, and carried a 13 percent premium to Blackstone's $33.50 offer.
Shares of LaSalle, which owns interests in hotels including Park Central San Francisco and Westin Michigan Avenue, were up 1.4 percent at $35.67.
LaSalle said its board will review Pebblebrook's proposal, and determine a course of action that is in the best interest of its shareholders.
Pebblebrook said its latest offer "takes into account" the $112 million termination fee LaSalle agreed to pay to Blackstone.
In May, LaSalle decided to sell itself to private equity firm Blackstone for $3.7 billion in cash, rejecting a cash-and-stock offer from Pebblebrook.
Pebblebrook said LaSalle shareholders will have the choice of receiving a fixed amount of $37.80 in cash for each LaSalle share they own, or 0.92 of a Pebblebrook share.
Pebblebrook said the cash part could be a maximum of 20 percent of the outstanding LaSalle shares. If the number of shares opting for cash exceeds 20 percent, those shareholders will be subject to pro rata cutbacks.
"It is clear that the value of our offer is substantially greater .... It is also clear that LaSalle shareholders expect to receive far more value for their shares than Blackstone's agreement," Pebblebrook Hotel Trust Chief Executive Officer Jon Bortz said.
Pebblebrook previously sweetened its $3 billion-plus offer in April, after LaSalle said the initial bid undervalued the company.
The Maryland-based company, which went public around a decade ago, owns several hotels, including InterContinental Buckhead Atlanta and The Westin San Diego Gaslamp Quarter.
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