NEW YORK - Giant oil company Chevron Corp (CVX.N) plans to restructure its refinery operations, cutting some jobs and exiting some markets, a company spokesman said on Tuesday.

U.S. refiners have been shutting down operations as the rising costs for crude oil squeeze margins and outpace increases in prices for refined products such as gasoline, heating oil, diesel fuel and jet fuel.

Chevron, the fifth-largest refiner in the United States, issued a memo to employees on Monday laying out the broad outlines of the downstream restructuring, which also includes lubricants and supply and trading. It is expected to be completed in the third quarter.

It's going to be a leaner organization with fewer positions, but we have not yet determined the number of positions we need, Chevron spokesman Lloyd Avram said.

The company will exit from certain markets, he said, although which markets the company will leave has not yet been determined.

Chevron has also not decided whether to close any of its refineries, he said. Further details are expected to be released in March.

Earlier this month, Chevron warned that its fourth-quarter results would be sharply lower than those of the previous quarter due to a further deterioration in refining margins.

The company operates more than 1 million barrels per day of refining capacity in the United States, including major plants at Pascagoula, Mississippi and El Segundo and Richmond in California, as well as refineries in Singapore, Thailand, South Korea and Wales.

Earlier this month, Royal Dutch Shell Plc (RDSa.L) said it will transform its Montreal East refinery into a fuel terminal. Leading U.S. refiner Valero Energy Corp (VLO.N) said in November it would permanently close its Delaware City, Delaware, plant, three months after it indefinitely shut its Aruba refinery.

Sunoco Inc (SUN.N) has also idled its Eagle Point, New Jersey, plant, and Flying J shut its Bakersfield, California, refinery a year ago.

Shares in Chevron dipped 0.5 percent to $78.83 in morning trade on the New York Stock Exchange. (Reporting by Matt Daily, editing by Gerald E. McCormick, Dave Zimmerman)