Interior Secretary Cecil D. Andrus is ordering oil and gas companies to agree to strict production schedules or face the unprecedented penalty of losing their leases on offshore drilling sites.

Andrus has told one company to begin pumping natural gas from its Gulf Coast site by the fall of 1978 or forfeit its lease with the federal government. When the lease-holder, Aminoil Oil Co. of Winston Salem, N. C., asked for a six-month extension in order to locate a drilling rig, Andrus gave it only four days. The company promptly located a rig.

The interior Secretary has scheduled a review of 60 other leases in the gulf which are not producing oil or gas and are scheduled to expire in the next few months. In each case, he could refuse to extend the lease unless its holder agrees to a fixed date for production.

Normally, the extension of a lease is virtually automatic decision made by a regional supervisor of the U. S. Geological Survey. No Gulf Coast lease has been canceled since drilling on federal offshore property began there in 1954. Andrus has ordered a review of all 60 by a departmental task force and has served notice he will make the final decision on renewing or canceling each lease.

His action is part of an overall Interior Department plan to press oil gas companies for increased production in the gulf.

Last month, he ordered an investigation of the gulf's natural gas field to determine whether companies are deliberately holding back gas and contributing to this winter's shortage. A preliminary inquiry, he said, showed that some fields had shut down production for no clear reason and that a total of 188 reservoirs with 767 billion cubic feet of natural gas were not producing.

Some critics have maintained gas producers are deliberately holding back their gas while awaiting deregulation on the assumption that prices would then rise. Andrus has not said he beleives that and the producers have denied it.

According to Interior, there are about 1,700 offshore oil and gas leases in the gulf but only about 800 of them are in production. Over the years, amny leases have been abandoned by the industry when they proved unproductive but none has been canceled by the United States.

The companies pay large bonus prices for the leases, giving them the right to explore for gas or oil for five years. Many are extended year by year at a price of $3 per acre - about $15,000 for a tract of average size.

Aminoil, a subsidiary of RJR industries, Inc., had paid $3.8 million for its lease in 1971 and had obtained a one-year extension which expired early last month. In drilling six exploratory holes, two of which promised to yield gas, the company estimated that it had located 21 billion cubic feet of natural gas and hoped to discover an additional 10 billion cubic feet. Without the additional discovery, it had contended, commercial production would not be profitable.

The agreement that Andrews reached early this month with Aminoil requires the company t drill its seventh hole and decide whether it wants to keep the lease. Ir it decides to keep it, Aminoil must commit itself by July 20 to construction of an oil-rig platform, which requires that production of natural gas from the site must begin by August, 1978.

The oil and gas industry's response to Andrus' new policy so far has been muted. American Petroleum Institute President Frank Ikard said yesterday he "would like to see how the policy evolves" before making a judgment on it.

A spokesman for Aminoil said the company did not consider the pressure by Andrus to be unfair. "We had very good negotiations with him," the spokesman said.