President Carter's request for rapid investigation of a United Auto Workers trade complaint against Japanese automakers was rejected tentatively yesterday by the International Trade Commission.

The UAW has called for a combination of quotas and higher tariffs to limit Japanese firms substantially expand auto production in this country, claiming that the U.S. auto industry has been gravely hurt by Japanese competitors.

Without taking a position on the complaint, Carter sought an expedited consideration of the UAW case by the ITC. If the ITC finds that U.S. automakers have been injured seriously by Japanese imports, it would recommend quotas or other action by the president to correct the problem.

Carter's request was part of a package of administration actions to aid the auto industry, announced by the president more than a week ago in Detroit. The request pleased the UAW, which has not endorsed a candidate in the presidential campaign yet. If the request were granted, the ITC's finding would have been made October 12, well before election day in November, confronting Carter with a decision of major political as well as economic significance.

But the ITC yesterday turned down the request by its chairman. William Alberger, to accelerate the investigation by 60 days. Alberger said the decision was tentative and that the commission would consider other appeals for a more rapid inquiry.

A line of applicants is forming for another part of the auto industry aid plan announced by Carter.

Detroit and Hamtramck, Mich., are looking for federal funds to help finance a $150 million conversion of an abandoned Chrysler Corp. auto plant into an industrial site for a new General Motors Corp. plant to manufacture Cadillacs, Detroit officials said.

At the Detroit meeting with auto industry leaders, Carter promised special federal assistance for communities hard-hit by the auto-sales collapse. The 70-year-old Dodge Main plant in Hamtramck has been shut down for good by Chrysler, but GM is willing to build a new plant if the Chrysler property and adjoining land in northeast Detroit can be cleared for reuse.

Demolishing the vast, eight-story Doge building may cost as much as $30 million, local officials say. In addition, some 1,500 homes must be acquired to create the new industrial site.