Anadarko Petroleum is reopening acquisition talks with Occidental Petroleum — two weeks after agreeing to sell itself to Chevron — setting up a possible faceoff over its prized shale oil assets in the Permian Basin.

“Anadarko’s board of directors, following consultation with its financial and legal advisers, has unanimously determined that the Occidental proposal could reasonably be expected to result in a ‘superior proposal’ as defined in the Chevron Merger Agreement,” the Houston-based company said Monday in a statement.

Anadarko accepted a $33 billion cash-and-stock deal from Chevron on April 12 that would have the California-based oil giant pay the equivalent of $65 per share. But Occidental countered last week with a $38 billion offer; the equivalent of $76 a share, half in cash and half in Occidental stock. Chevron’s deal calls for 25 percent cash.

If Anadarko formally declares it has received a “superior” offer, Chevron would have four days to make a counterproposal, according to the terms of their agreement. The deal also includes a 3 percent breakup fee, which would come to about $1 billion.

Anadarko said that its agreement with Chevron remains in effect and that there is no guarantee Occidental’s proposal is better for shareholders. But Monday’s overture raises the question of whether Chevron — which reported nearly $15 billion in earnings last year and is five times the size of Occidental in terms of market capitalization — will sweeten its offer.

The acquisition would make Chevron the second-largest crude producer in the world and capable of churning out an estimated 3.9 million barrels of oil equivalent per day. “We believe our signed agreement with Anadarko provides the best value and the most certainty to Anadarko’s shareholders,” Chevron said in a statement Monday.

Anadarko’s shale assets in the Permian Basin — an oil-rich area spanning west Texas and southeastern New Mexico — are prized by both companies. Analysts say Chevron’s global assets, including deepwater drilling and liquefied natural gas, make it a better strategic fit for Anadarko.

”Anadarko is angling for a better bid from Chevron,” said analyst Stewart Glickman of CFRA Research. “I think Chevron will sweeten their offer a bit, but they don’t have to match Oxy. The strategic fit (with Chevron) … just makes more sense. Chevron has a better war chest, better complementary assets. Anadarko probably knows this.”

In a report issued Monday, Jefferies analyst Jason Gammel downgraded Occidental stock to a “hold.” “Oxy’s hostile counter-offer for Anadarko is a risky but perhaps necessary move against a better-capitalized bidder for a company that rejected its initial overtures,” Gammel said in his report. “We expect that Oxy’s stock could come under further pressure regardless of whether it is ultimately successful in its APC bid or not, and downgrade the stock to Hold. We believe the market has already priced in a higher bid from Chevron and maintain our Buy rating.”

Analyst Bill Selesky of Argus Research said Anadarko is bound by its responsibility to shareholders to explore Occidental’s latest offer.

“They have to listen to what other potential buyers are saying,” Selesky said. “They have to act in the best interests of their shareholders. This doesn’t surprise me.”

Chevron and Anadarko shares both posted gains on Monday. Chevron climbed 64 cents, about 0.55 percent, to $117.72, and Anadarko rose 21 cents, or 0.29 percent, to settle at $72.93. Occidental shed $1.18, or 1.92 percent, to close at $60.13.