The White House has ordered a State Department review of efforts to tighten controls on the sale of oil and gas exploration equipment to the Soviet Union, high administration sources said yesterday.

The White House order, contained in a memo sent Wednesday by Presidential National Security Adviser William P. Clark, appears to be an attempt to dampen an increasingly bitter battle within the Reagan administration as hawks tried to use the Soviet downing of a Korean airliner to push through tougher controls on exports to Russia.

That move last week by an interagency committee headed by Assistant Commerce Secretary Lawrence J. Brady, a leading foe of trade with the Soviets, was reported to have angered his boss, Commerce Secretary Malcolm Baldrige, and Secretary of State George P. Shultz. Baldrige and Shultz have been working to coordinate curbs on the sale of oil and gas exploration equipment to the Soviets with the United States' allies of Western Europe and Japan.

While not taking any position on the Brady committee action, Clark was reported by high administration sources yesterday to continue his support for the Shultz-Baldrige policy of working toward multilateral, not solely American, controls on the sales of strategic equipment to the Soviets.

The Brady committee recommendation would in effect give the Defense Department a veto on sales of 17 categories of oil and gas exploration equipment to the Soviets by placing them under the tougher national security controls instead of the foreign policy criteria they now fall under. Industry sources said America's European allies strongly opposed those tighter controls when they were first recommended early this winter.

The committee also was reported to have recommended against issuing a license to a Hughes Tool Co. subsidiary to sell $40 million worth of submersible pumps to the Soviets. While administration officials called submersible pumps a highly sensitive export whose technology should be kept from the Soviets, industry sources said they are off-the-shelf items readily available to Russia from many foreign suppliers.

The Petroleum Equipment Suppliers Association asserted in a telegram to the president yesterday that the Brady committee recommendations "appear to be another counterproductive and futile government action . . . that ignores the foreign availability of most petroleum equipment."

The fight comes as Congress is about to begin debate next week on the renewal of the Export Administration Act--the law allowing controls on the sale of strategic goods overseas--which expires Sept. 30. The House bill proposes far less stringent curbs than the administration wants, largely due to a lobbying campaign sparked by business' contentions that the use of export curbs against the Soviets by the Carter and Reagan administrations has hurt America's industries more than they have hurt Moscow.

At a Commerce Department meeting Tuesday night, Brady was reported to have urged stronger efforts to replace the House bill with stiffer controls.