An investment firm trying to displace a California bank from acquiring Hawaii’s fifth-largest bank has upped its offer for the parent of Territorial Savings.

Blue Hill Advisors LLC announced Thursday that it is offering to pay $12.50 per share for Territorial Bancorp Inc., up from $12 in its initial unsolicited bid.

The cash offer aims to derail a pending acquisition of Territorial by Los Angeles-­based Hope Bancorp Inc., which was agreed to in April by Territorial’s board of directors.

Blue Hill calls the Hope deal a “fire sale” that Territorial shareholders should reject.

Under the merger agreement with Hope, Territorial shareholders are to receive 0.8 share of Hope stock in exchange for each Territorial share they own.

Territorial’s board rejected the initial bid by Blue Hill twice — on Sept. 6 and 12 — citing merger terms with Hope that restrict the pursuit of competing proposals unless they are “reasonably likely” to lead to a superior proposal. The board largely questioned the ability of Blue Hill to complete a purchase.

Blue Hill is an investment advisory firm, and its acquisition effort involves investors and former Bank of Hawaii CEO Allan Landon.

Territorial has about $2 billion in assets and operates 28 bank branches on Oahu, Maui, Kauai and Hawaii island.

Hope operates Bank of Hope, which has 48 branches in California, Washington, Texas, Illinois, New York, New Jersey, Virginia, Alabama and Georgia. The company has about $17 billion in assets.

Territorial stockholders are scheduled to vote on the Hope acquisition Oct. 10 at a special meeting.