President Reagan yesterday overruled the International Trade Commission and said that batteries made in Duracell Inc.'s Belgium factory could continue to be imported, even though Duracell's parent company wants to keep them out.

The Belgian-manufactured Duracells are not sold directly to U.S. wholesalers from the European plant. Instead, companies that normally do business with the Belgian Duracell operation either sell some of their purchases to U.S. wholesalers or to a third-party that sells them here.

Even though the batteries can pass through two or three hands before arriving here, the dollar is so strong that the batteries still cost less than they would if purchased from the U.S. Duracell factory.

Dart & Kraft Inc. owns both Duracell Inc. and Duracell's Belgian subsidiary. The Chicago-based consumer products company had argued that the imports infringed on its territorial rights because it owns the U.S. trademark to Duracells.

The U.S. Customs Service has long held that if a product is made by one of its subsidiaries, the U.S. company cannot claim infringement.

The U.S. International Trade Commission agreed with Dart & Kraft and recommended to the president that he ban imports of Belgian Duracells. Reagan disapproved that decision yesterday, but called for public comment.

The Duracell question is one wrinkle in the so-called gray market, in which some U.S. importers legally purchase foreign name-brand products abroad at a lower price than licensed U.S. distributors of those products can buy them from the manufacturer.

In some cases, products can be purchased more cheaply at retail in foreign countries than licensed U.S. distributors can buy them at wholesale. The gray market involves such products as cameras, automobiles, watches and perfume.

Dart & Kraft said its case did not involve the gray market because Duracell is a U.S. brand name, not a foreign brand name.

For the most part, it is the strong dollar -- which makes foreign products so inexpensive in terms of the U.S. currency -- that gives most of the boost to the gray market.