HOUSTON — In an escalating bidding war, Anadarko Petroleum said on Monday that it intended to reject its first suitor in a takeover bid, Chevron, after Occidental Petroleum came forward with a better offer.

The announcement by Anadarko’s board, a day after Occidental sweetened its bid with more cash, is far from a final decision. Chevron will now have four days to improve its offer, after which Occidental would have several days to revise its bid.

Bidding wars for big oil companies have been rare in recent years, and the Occidental-Chevron standoff has already seized the investment world’s attention. Occidental’s chief executive, Vicki Hollub, has emerged as one of the nation’s most prominent oil executives by challenging Chevron, a giant four times the size of her company.

“Known for her love of Alabama football, Oxy C.E.O. Vicki Hollub is ripping up the playbook and running an all-out offense on the Anadarko board,” Paul Sankey, an oil and gas analyst with Mizuho Financial Group, wrote in a research note to clients on Monday morning.