General Motors Corp. and Toyota Motor Co. Ltd. have formally requested federal approval of their plan to produce small cars in the United States, GM officials said yesterday.

The joint-venture proposal was submitted on Monday to the Federal Trade Commission, which must review the agreement for possible violations of U.S. antitrust laws before it can take effect.

The formal submission came nearly two months after GM and Toyota signed a historic "agreement in principle" to produce small, front-wheel-drive cars at an idle GM plant in Fremont, Calif. Both companies, equal partners under the $300 million joint-venture pact, want to start production of a 1985-model car as early as possible in 1984.

The FTC will not complete its review of the GM-Toyota plan until mid-June, largely because the agency probably will request additional information from the two companies, FTC sources said yesterday. The request for more information, called the "second request" in agency jargon, will tack an additional 20 days onto the initial 30-day review period, the sources said.

"A second request is to be expected in a deal this big and complicated. It is improbable that the commission will take any final action without a second request," one agency source said.

Under federal law, joint-venture and similar agreements cannot take effect for at least 30 days after proposals are submitted to the FTC. After that period, the commission could take no action, tacitly allowing implementation of the the proposal. It could seek a federal court injunction against the agreement, thereby delaying its implementation for an indefinite period, and possibly killing the agreement altogether. The commission could also issue an administrative complaint, objecting to certain portions of the pact and, as a possible byproduct, providing support for privately initiated suits. Or, the commission could issue a second request, extending the review period.

Commission sources said yesterday that a second request should not be interpreted as a sign that the FTC in any way objects to the GM-Toyota pact.

Implementation of the plan, under which GM and Toyota would turn out 200,000 small cars annually, also depends on approval of a labor agreement between the new joint-venture company and the United Auto Workers union. UAW leaders already have had a number of discusions with GM officials, but have not had any significant contact with Toyota officials on the matter of UAW representation at Fremont.