HOUSTON — Occidental Petroleum fortified its bid for Anadarko Petroleum on Sunday night with more cash in its latest effort to outbid Chevron and win the support of Anadarko’s shareholders who may well make the final decision on a merger.

In a letter to Anadarko’s board of directors, Occidental’s cash-and-stock proposal remained at $76 per share, or $38 billion. But the cash portion was raised to 78 percent from 50 percent.

Chevron may now raise its bid, but it did not have an immediate comment on Occidental’s new move.

Vicki Hollub, Occidental’s chief executive, said her company’s proposal represented a 23.3 percent premium over Chevron’s bid.

“The significantly increased cash component provides value,” she wrote in the letter to Anadarko. “We hope we can execute this merger agreement without delay and proceed to bringing this exciting combination to fruition.”