"We suspended production for a little bit. We're in the process of restarting," Morris said. He said he couldn't give a timetable for when the crude oil unit would be running again.
Officials said they didn't know what caused Monday's fire at the refinery in Big Spring, about 300 miles west of Dallas.
Earlier Monday, Alon announced it had restarted several parts of the refinery and was producing gasoline, diesel and asphalt. However, the refinery was only operating at 35,000 barrels per day -- half its normal capacity.
Five people were hurt when an explosion rocked the refinery on Feb. 18, sending black smoke billowing into the sky and closing schools and an interstate highway.
The injury count might have been reduced because only 40 people were working on the President's Day holiday instead of the usual crew, which is four times as large, company officials said at the time.
Morris said Alon was ahead of its own schedule in returning the refinery to full production and hoped to return another key unit running by mid-July.
The company said it had inspected that part of the plant, called a fluid catalytic cracking unit, and wouldn't need to wait for any major replacement equipment.
Two other units that are still under repair should return to production after the cracking unit, Morris said. One of those units produces octane for premium gasoline, and the other makes byproducts used in plastics.
Morris said insurance would cover Alon's cost of repairs, which he declined to estimate. He said about 800 workers have been hired for the reconstruction project -- more than four times the refinery's normal work force.
The Big Spring refinery is one of four refineries operated by Alon in Texas, California and Oregon.
Dallas-based Alon, whose majority owner is Alon Israel Oil Co., earned $104 million last year on revenue of $4.54 billion. The company depends on the refinery for 60 percent of its gross income, according to Standard & Poor's Ratings Services.
The company makes and sells petroleum products under the FINA brand in several southern and western states and supplies some 7-Eleven stores.
Shares of Alon rose Monday morning but then fell to close lower by 69 cents, or 4.2 percent, at $15.64.