Saudi Arabia, the world's leading oil exporter, has cut its record oil production by more than 1 million barrels a day in recent weeks, pushing world oil markets -- already tight because of the Iranian shutdown -- toward a serious shortage.

During most of December and the first 2 1/2 weeks of January the Saudis were producing nearly 10.5 million barrels of oil a day. During mid and late 1978 production ranged from more than 7 million to nearly 9 million barrels a day.At a Jan. 15 meeting with members of the Arabian American Oil Co., however, the Saudis ordered production limited to 9.5 million barrels a day. Beginning Jan. 20, Saudi production dropped from well above 10 million to 8.6 million barrels a day.

Reports of the Saudis' sharply reduced oil production in the general and trade press, as well as in industry circles, have been denied or minimized over the last week by senior Carter administration officials.

Administration officials, including Energy Secretary James R. Schlesinger, have repeatedly said that a sharp increase in production by Saudi Arabia has been critical in making up some of the more than 5 million barrels of oil a day lost when political turmoil closed Iran's oil fields.

If Saudi Arabia holds to a ceiling of 9.5 million barrels a day, as it has told American oil companies operating there, the White House and Energy Department will be forced to face the possibility of stern conservation measures earlier than officials expected.

In a further blow to the administration's plans to offset the impact of the Iranian crisis, the Saudis told the arabian American Oil Co. (Aramaco) that oil produced in excess of the first 8.5 million barrels of oil each day will be sold at $14.55 a barrel, $1.21 above the current world market.

Administration officials say that some of the production cuts could be the result of needed maintenance in the Saudi fields, while industry executives say that the cutbacks reflect stern conservationist pressures within the Saudi government and a political response to American pressure on the Saudis to support the Camp David Middle East peace initiative.

Oil industry executives say they expect the news of the Saudis' orders to Aramco to increase oil prices on the so-called spot market, which includes oil not sold under long term contract. Prices on the spot market have been reported as high as $18- $20 a barrel.

Asked last week whether the Saudis intended to limit production to 9.5 million barrels a day, Schlesinger told reporters, "I think not. There is some question whether that will be the case."

Asked the same question yesterday during Senate Energy Committee hearings, DOE's David J. Bardin said, "We are monitoring that situation closely. We have no reason to believe the Saudis would not be able to maintain 10 million barrels a day."

Petroleum Intelligence Weekly, an authoritative industry newsletter, reported yesterday that Saudi oil production dropped from 10.3 million barrels on Jan. 9 to 8.6 million barrels on Jan. 20, and did not rise above that level through Jan. 27.

The Aramco companies, Exxon, Texaco, Mobil, and Standard Oil of California, have repeatedly declined to comment on Saudi production in recent weeks.

In a related development, Bardin told the Senate Committee DOE would send its standby rationing plan and standby mandatory conservation plans to Congress Feb. 26. Bardin said that "we are not going to make the decision to shift to mandatory allocations at this time," and that DOE is appealing for voluntary conservation and industry cooperation to reduce energy demand and share available supplies.

Bardin also said that gasoline coupon rationing, which would take six to eight months to implement and $1.5 billion a year to administer, "is a rough and ready kind of equalizer" for managing the shortage.

Senate committee members, including Dale Bumpers (D-Ark.) and J. Bennett Johnston (D-La.), criticized the administration for its delay in sending standby emergency plans to Congress.