The Metro board yesterday approved a $423.2 million operating budget for the next fiscal year that is designed to hold the line on bus and subway fares.

The action fulfilled a pledge by Metro General Manager Carmen E. Turner, who has called for keeping fares "affordable" to "encourage ridership." The fares, which were increased June 30, are not expected to be raised again before mid-1986.

Under the new budget, the transit system's deficit would climb to $220 million in fiscal 1986, a 7.2 percent rise over the anticipated shortfall for the current fiscal year. Metro's deficits are financed mainly by county and city governments from tax revenues.

The budget, which was reviewed by local governments in the past month, reflected a series of cost-cutting efforts by Turner and board members, including what was described as a 5 percent reduction in administrative overhead. Turner has termed it "probably the tightest budget" ever for Metro.

In another development, the board awarded a controversial contract for more than $900,000 in carpeting for subway cars to a District firm over sharp protests from one board member. "It's going to cost the authority more money than it ought to," charged Alexandria City Council member Donald C. Casey.

Subway carpets have long been a focus of debate. Some officials previously contended that Metro could save money by switching from carpets to rubber-like flooring. The new contract, awarded to Randy's Carpet, is aimed at replacing worn and discolored carpets on 250 older rail cars.

Casey argued that all bids on the contract should have been turned down. Metro officials acknowledged that errors were made in drafting the proposal, but described the award as proper. Jawad F. George, a lawyer for another bidder, Park Carpet of Falls Church, said the firm plans to sue Metro.

In awarding the $923,370 contract, Metro officials rejected a lower price from Contract Distributors Corp. of Bethesda, which submitted an $808,500 bid. Metro officials said the company failed to agree to a two-year payment schedule and had sought to be paid immediately.

In other developments:

* A Metro committee gave preliminary approval to a plan to offer cut-rate passes to families and tourists for bus and subway trips on weekends and holidays. Under the proposal, a group of four people could buy the passes for unlimited rides on a Saturday, Sunday or holiday. A four-pass package would cost $5.

* The board voted to seek federal approval to buy an additional 72 Italian-made subway cars at an estimated cost of $84 million without competitive bidding. A federal official said the issue will be reviewed.