Stock prices pulled back today, faced with renewed upward pressure on interest rates.

The Dow Jones average of 30 industrials, up 8.48 points on Tuesday, fell 7.14 to 1,863.29. At its midsession low, the average was down about 20 points.

Volume on the New York Stock Exchange came to 116.96 million shares, against 114.71 million Tuesday.

Interest rates declined briefly at today's opening, but then resumed their recent rise as conjecture spread that the Federal Reserve Board was reluctant to ease credit further.

Prices of long-term government bonds, which move in the opposite direction of interest rates, dropped $10 to $20 for every $1,000 in face value.

Meanwhile, the oil market came under pressure. The price of crude oil for July delivery slumped 77 cents to $13.10 a barrel on the New York Mercantile Exchange.

But analysts said many traders were skeptical that oil prices were returning to the kind of sustained decline that took place earlier this year.

Many observers now believe the stock market must draw its inspiration from a fresh source, such as improving corporate profits, if it is going to resume the dramatic rise it staged from last fall through the first quarter of 1986.

However, the evidence is less than conclusive to date that earnings will pick up enough momentum in the months ahead to stir up widespread enthusiasm for stocks.

On the trading floor, Sperry topped the NYSE active list, losing 1/8 to 74 3/4.

Among actively traded blue chips, International Business Machines fell 2 3/4 to 150; American Telephone & Telegraph 1/8 to 24 1/2, and Eastman Kodak 1/4 to 61 1/4.

Energy stocks declined along with oil prices. Amoco lost 1 1/8 to 62 3/4; Exxon 3/4 to 59 5/8; Atlantic Richfield 1 3/8 to 53 3/8; Chevron 5/8 to 40 1/4, and Mobil 1/2 to 30 7/8.

Commonwealth Edison dropped 7/8 to 30. The company said it had shut down a unit at its LaSalle nuclear power plant after a malfunction on Sunday.

Auto issues declined as domestic car makers reported lower sales for the last part of May. General Motors fell 7/8 to 78; Ford Motor 5/8 to 53 5/8, and Chrysler 3/8 to 36 1/4.

Bank stocks also were weak, with J. P. Morgan down 1 3/8 at 85 5/8; Citicorp down 7/8 at 60 1/4; Chase Manhattan down 5/8 at 42 1/8, and Chemical New York 1/8 lower at 52 1/2.

In the semiconductor group, Texas Instruments dropped 1 1/8 to 135 1/2, National Semiconductor lost 1/2 to 13 1/2 and Motorola added 1/8 to 45 3/4.

Insurance stocks rebounded after a two-day sell-off. American International Group jumped 2 1/8 to 125 3/4 and Aetna Life added 1 3/8 to 61 1/4.

In the overall tally on the Big Board, about nine issues declined in price for every five that gained. The exchange's composite index dropped 0.84 to 140.20.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 138.43 million shares.

Standard & Poor's index of 400 industrials fell 1.80 to 273.20, and S&P's 500-stock composite index was down 1.57 at 243.94.

The Nasdaq composite index for the over-the-counter market lost 0.43, to close at 399.05. At the American Stock Exchange, the market value index closed at 280.00, down 0.48.