The D.C. City Council, acting on an urgent request from Mayor Marion Barry, preliminarily agreed yesterday to issue tax-exempt bonds to help a California company build a restaurant on the Southwest waterfront -- the first such commercial use of the District's bonding authority.

Previously, the District has issued such bonds only to aid George Washington University. Issuing the bonds requires no cash outlay by the city, but the use of tax-exempt bonds in other cities on behalf of commercial enterprises has been criticized as amounting to a government subsidy.

Yesterday's request from Barry, which came to the council only late Monday, was the first of more than a dozen planned uses of such bonds for commercial projects in Washington, according to Lawrence P. Schumake, executive director of the city's Office of Business and Economic Development.

If the transaction is formally approved by the council next year, the city would endorse the sale of $3.5 million in industrial revenue bonds for the restaurant proposal by Special Restaurants Corp., a Long Beach, Calif., company that listed $55.8 million in assets in its 1981 annual report. The bonds would be exempt from federal taxation.

The action came during the council's last session of the year and its last under outgoing Chairman Arrington Dixon. The council acted on a wide variety of issues, including allowing the city to borrow up to $150 million to cover cash shortages. A bill to give the council virtual veto power over any amendments to the proposed statehood constitution was put off until next year.

The proposed bond issue was passed by the council on a voice vote, but was criticized by some members who said they did not have enough information about it and feared it might anger Congress.

Earlier this year, Congress tried to curb abuse of such bonds by prohibiting the 50 states from using revenue bonds for a variety of kinds of businesses, including restaurants, after this year.

Barry, in an interview after the council session, said the restaurant proposal was being rushed to meet the congressional deadline and because he had ordered all such projects held up until after the fall elections "to avoid any hint of politics."

Schumake told the council that although the District was not specifically included in the new federal law, the mayor and his office believed that the council should immediately "signal its intent" to approve the restaurant.

Council member John A. Wilson (D-Ward 2), chairman of the Finance and Revenue Committee, called the administration's plan "slipshod" and said the city was risking irritating Congress for a small project it had not yet justified. The waterfront area is in Wilson's ward.

The proposal must formally come before the council next year and will be the subject of hearings. Schumake said Congress also must agree on each project. "There will be plenty of time for review by all concerned," he said.

The restaurant corporation hired local lawyer David Wilmot, a friend of the mayor and a bidder on other development projects, to aid its proposal. Wilmot could not be reached for comment. Barry said he was not aware of Wilmot's participation in the project until after the election. "He's a lawyer, he's got to do lawyer work," Barry said.

Schumake said he knew of no local investors in the restaurant.

In other action, the council voted to give Dixon, who was defeated in the September Democratic primary by David A. Clarke, $25,000 to spend on his transition from the council to private life.

The council also approved a measure establishing standards for real estate licenses, a bill to tighten child custody procedures and require the use of car safety restraints for children under 6, penalties for defacing religious properties, and a proposal to allow staggered car registration in the city.

Another measures would establish standards to allow the mayor to close some public alleys -- a power now held only by the council.