Steel companies began cutting production and laying off workers yesterday as thousands of Teamster haulers continued their week-old wild-cat strike and union leaders prepared to give the walkout their official sanction:

Republic Steel Corp. began furloughing workers at several Ohio finishing plants and planned to shut the facilities shortly, company officials said. National Steel Corp. said it is planning to cut back sharply on finishing work and lay off 3,000 workers by Sunday. Wheeling-Pittsburgh also said weekend layoffs are likely.

Many of the 10,000 to 15,000 Team-ster-organized steel haulers refused to go back to work after the union tentatively agreed to a new master freight contract last week but failed to reach agreement on a contract "rider" for the steel haulers.

The steel haulers, most of whom own their trucks, are demanding a return to their pre-1976 system of pay per load of steel and a separate vote on the steel agreement.Under existing rules, all 300,000 Teamsters covered by the industrywide contract vote on the contract and all its supplements, including the steel rider.

Earlier this week, Teamster officials were branding the walkout a "wildcat strike" and demanding that the steel haulers return to work.

But, as negotiations on the steel agreement failed to produce a settlement and the steel haulers continued to defy the order, Teamster officials to defy the order, Teamster officials indicated late Wednesday that the strke would probably receive official sanction.

Teamster President Frank E. Fitzsimmons is "totally behind" the steel board is "in a mood to sanction the haulers and the union's executive strike," union spokesman Bernard Henderson said yesterday. He said a three-step sanctioning process is under way and could be completed by early next week.

Ballots for ratification of the agreement are scheduled to be mailed April 25 and counted under Labor Department supervision on May 11, Henderson said The steel rider will be voted on later if it is not negotiated by the time ballots are mailed, he added.

Union and company officials have estimated that the proposed new contract provides wage and benefit increases of at least 30 percent over three years. Using a different method of calculation, the Carter administration has said the pact is within the government's anti-inflation guideline of 7 percent a year.

The steel haulers have a long history of militancy and internal disagreements with the Teamsters' leadership, including a demand for greater autonomy within the union. Their current strike appears to be having more effect than an earlier walkout organized by the Fraternal Association of Steel Haulers (FASH) in December.

While officials of U.S. Steel, Behtlehem Steel and several other large companies said they had no immediate plans to curtail production, they said cutbacks could come next week if the strike continues.