In a strongly worded letter sent late Thursday, one of the largest shareholders of First California Financial Group Inc. called on the board to sell the bank holding company.

Gideon King, president and chief investment officer of Loeb Capital Management, criticized the Westlake Village company’s decision to reject a recent acquisition offer and said his firm has “grown increasingly frustrated” with the board’s seeming reluctance to engage prospective buyers.

“At no point has (the board) simply stated that it is engaged in a process to explore strategic alternatives to maximize shareholder value,” King said in the letter, which was released as markets closed. “Rather, we believe shareholders have been subjected to vague press releases that give shareholders no assurance that the board takes its fiduciary duties seriously.”

First California did not return a call requesting comment.

On May 3, PacWest Bancorp in Century City offered to buy First California for $7.25 per share, a 32 percent premium over its closing price at the time. First California released a statement at the time declining the offer and suggesting there were other strategic alternatives.

The decision was criticized by shareholders, including Boston’s Castine Capital Management, which reduced its stake in the company by half.

King said his letter was prompted by the company’s second quarter earnings announcement Thursday, which did not provide details about the bank’s strategic plan.

“We no longer will give this management team and board the benefit of the doubt,” he said. He also cited “an adversarial relationship between the owners and operators” of the bank.

Loeb, headquartered in New York, is First California’s third largest shareholder, with about 2 million shares, or a 7 percent stake.

First California’s shares closed at $6.54, down 3 percent during the day.