Stock prices declined broadly today in selling blamed on uncertainty over the outlook for the economy and interest rates.

Trading set its slowest pace since the July 5 session, which fell between the Independence Day holiday and a weekend.

The Dow Jones average of 30 industrials dropped 6.16 points to 1,346.89.

Volume on the New York Stock Exchange totaled 79.61 million shares, compared with 87.86 million in the previous session. On July 5, 62.45 million shares were traded.

Analysts said investors were uneasy about the prospective reception the credit markets will give to the Treasury's record offering this week of $21.5 billion in bonds and notes. The concern is that interest rates might have to move up to attract enough buyers.

At the same time, hopes that economic growth was reviving got no support from a survey of corporate purchasing executives, the results of which were reported over the weekend. The National Association of Purchasing Management's index was unchanged from its reading in June, at a level that is interpreted as indicating a declining economy.

That was at variance with other recent data -- including a rise in the government's index of leading indicators -- that have prompted hopes for a pickup in economic activity and corporate profits in the third quarter of the year after a sluggish first half.

Most of the market's losses came in the first half of the session. Stocks showed no adverse reaction after President Reagan said he had a small patch of skin cancer on his nose.

MGM-UA Entertainment jumped 4 3/4 to 22 5/8 after the company said it was discussing a possible deal under which it would be acquired by Turner Broadcasting System for $29 a share in cash.

Beatrice Cos. led the active list, up 2 at 32 1/4 on turnover of more than 2.5 million shares. Over the weekend, the resignation of the company's controversial chairman and chief executive, James L. Dutt, was announced.

Second-most-active Trans World Airlines gained 1/2 to 22 5/8. Financier Carl Icahn, who owns more than a third of the company's stock, said he would bid $24 a share in cash and securities for the rest, seeking to preempt a previous merger plan under which Texas Air would acquire TWA.

Eastern Airlines was third, up 1/4 to 11 3/4. Pan American World Airways, American Airlines and UAL Inc. eased.

Manville Corp. fell 1 3/8 to 6 1/2 after a federal bankruptcy judge adjourned until Aug. 13 a hearing on Manville's proposed $2.5 billion plan to settle asbestos-related claims. Manville's board approved the plan Friday.

Tandy, which said it expected its purchase of the Video Concepts store chain to increase its sales by $150 million to $200 million in the fiscal year that began this month, rose 1 3/8 to 33 1/4.

The daily tally on the Big Board showed about five losers for every two stocks that gained ground. The exchange's composite index declined 0.58 to 110.27.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 96 million shares.

Standard & Poor's index of 400 industrials fell 0.78 to 212.40, and S&P's 500-stock composite index was down 0.86 at 190.62. The Nasdaq composite index for the over-the-counter market dropped 2.39 to 302.14. The American Stock Exchange market value index closed at 224.12, down 0.92.