With large investing institutions leading the way, the Dow Jones Industrial Average soared today to 1,249.10, a new all-time high, eclipsing by a point the measure's three-month-old record.

In heavy trading, stocks moved up sharply today as the Dow gained more than 15 points in a zig-zag trading session. Volume on the New York Stock Exchange totaled 103.05 million shares, up sharply from the 85.6 million shares traded yesterday.

"The leadership came from large, capitalized institutional-type stocks, primarily business sensitive and cyclical issues," said Robert Nurock an analyst with Investor's Analysis Inc. of Paoli, Pa. Nurock attributed the gain to a widely held view that the Federal Reserve Board has become more "accommodative" in its interest rate policies.

Analysts generally said that no particular events moved stocks higher today and that in fact the record-breaking performance came on a day when the news was negative, particularly on the foreign-policy front.

Over the last three trading sessions, the Dow industrials have picked up 34 points, a trend that has surprised many stock analysts who have been suggesting caution in recent weeks.

But today's move, apparently spurred in large measure by a lessening of fears about interest rates, brought along other stocks, such as those in the transportation industry. The Dow transportation index was up 7.20 points, closing at 590.04, just 0.59 point from that measure's all-time high.

Nevertheless, the gains were part of what Bear, Stearns & Co. analyst Dana Stewart called "a very orderly uptrend" going back to mid-August. "We are looking for the market to continue in this type of a saw-tooth pattern," he said.

Market activity was dominated by widely-held issues, with 20 of the 30 stocks that make up the Dow average posting gains, five falling, and five remaining unchanged.

Advancing stocks outnumbered declining stocks by a 987 to 582 tally. The New York composite index rose only slightly, up 0.79 point to close at 97.88 and the average price per share gained 30 cents.

Of the heavily traded stocks, American Telephone & Telegraph gained 3/4 closing at 67 3/4, Merrill Lynch was up 1 5/8 to 39 1/4 and Ford was up 1/2 to close at 63 1/2. Railroad and air-line stocks also showed gains with CSX, for example, up 2 1/4 to 77 and USAir up 1 1/8, closing at 30 1/2.

On the American Stock Exchange, the composite index rose by only 1.01 points, closing at 237.63. Volume rose sharply to 8.5 million shares, up from Monday's total of 6.8 million shares. The average price per share on the Amex rose seven cents with 311 stocks rising and 287 declining.

On the over-the-counter market, the Nasdaq composite index rose by 1.53 points, closing at 303.36 with 870 issues there advancing and 627 declining. Another 2,239 Nasdaq stocks were unchanged.