Standard & Poor's, the major New York bond rating service, gave the long-run prospects of the nation's steel industry another small vote of "no confidence" yesterday by downgrading the rating of U.S. Steel Corp. from AA to AA-minus.

U.S. Steel, the nation's largest steel producer, is the latest of several major steel companies to be downgraded slightly by Standard & Poor's.

The downgrading comes despite evidence of a strong recovery in the steel industry, a recovery in which U.S. Steel is sharing as capital investment spending picks up and automobile and appliance makers continue to order at high levels.

The AA-minus rating, nevertheless, is a relatively strong one for corporate issues. The top Standard & Poor's rating is AAA.

Alfred Rudd, the rating officer for Standard & Poor's, said that U.S. Steel "remains in basically the same category. We have reduced it to the low end of that category. We have some doubts as to the ability of the recovery [in steel orders and therefore in steel earnings] to bring debt protection back to the levels of 1974 to 1976."

Rudd said the major factor that convinced S&P to lower U.S. Steel's rating slightly was the 40 percent increase in long-term debt U.S. Steel has incurred in the last 18 months with a concomitant increase in internal costs.

U.S. Steel's rating had been reduced from AA to A in 1971, but was restored to a AA in 1976 after worldwide steel shortage in 1974 pushed nearly all U.S. companies, including U.S. Steel, into very high profits.

Since 1976, however, the steel industry has suffered the delayed effects of the 1975 recession, and only in the last few months has demand picked up again.

Rudd noted that S&P reduced the rating on several steel companies last year. Inland of Chicago was lowered to AA-minus from AA, while Bethlehem was reduced from AA to A and National from AA to A-plus.

A lower bond rating generally means that a company will have to pay a slightly higher interest rate the next time it tries to sell bonds. Steel companies often sell industrial revenue bonds and pollution bonds to finance new facilities.

Ray Hughes, first vice president of the investment banking firm of Blyth Eastman Dillon & Co., said the lowered rating also often will cause portfolio managers for institutional investors such as pension funds or mutual funds to re-evaluate a stock to see if it should be kept in the portfolio.

Hughes said he would not be surprised if Standard & Poor's, or the other major rating service, Moody's, lowered other steel company ratings. Hughesnoted that most analysts expect some sort of an economic turn-down in the first half of 1979 that will hurt steel orders.

Furthermore, he said that imports - the major impediment to industry earnings - do not seem to be moderating such despite a government program to set minimum prices for foreign steel.

U.S. Steel confirmed that it had been notified by Standard & Poor's of the downgrading, but otherwise had no comment.

The company has said that after losing money in the first quarter - largely because of the coal strike, but also because of slow orders - it expects a sharp rebound in the current quarter.

U.S. Steel Chairman Edgar Speer has said that after operating below 80 percent of capacity in the first quarter, the steel giant expects to operate above 90 percent in the second quarter.

Steel makers operate with high fixed costs, so profits rise quickly when volume picks up sharply because the fixed costs can be spread over more units of output.

Steel makers also have increased prices by about 6.5 percent this year and have scheduled another 3 percent rise on most of their products - expect for tin mill products used in making beverage containers - for July 30.