NEW YORK (AP) _ The stock market surged ahead today, making a run at the 2,500 level in the Dow Jones industrial average with a push from falling interest rates.

The Dow Jones average of 30 industrials, which closed Thursday at a new post-crash high, climbed 29.70 to 2,499.82 by 3 p.m. on Wall Street.

The last time the average closed above 2,500 was Oct. 13, 1987, when it stood at 2,508.16 six days before the crash on Black Monday.

Gainers outnumbered losers by more than 2 to 1 in nationwide trading of New York Stock Exchange-listed issues, with 1,008 up, 488 down and 483 unchanged.

Interest rates declined in the credit markets today. Prices of long-term government bonds, which move in the opposite direction from interest rates, posted gains ranging to more than $5 for each $1,000 in face value.

That served to reinforce spreading hopes on Wall Street that the Federal Reserve would succeed in its effort to engineer a ''soft landing'' for the economy - restraining inflation without causing a recession.

Analysts said the market also seemed to be benefiting from a sort of bandwagon effect.

The recent gains in the market, they noted, have put pressure on money managers who have been holding large cash reserves to try to catch up with the performance of their fully invested competitors.

Gainers among the blue chips included General Electric, up 3/4 at 54; American Telephone & Telegraph, up 3/8 at 35 1/2 ; General Motors, up 3/8 at 42, and McDonald's, up 2 1/8 at 59.

Avon Products led the active list and dropped 5/8 to 32 3/8 on top of a 7 1/8 -point slide Thursday, after Amway dropped its hostile $39-a-share bid for the company.

The NYSE's composite index of all its listed common stocks rose 1.66 to 178.95. At the American Stock Exchange, the market value index was up .93 at 353.51.

Volume on the Big Board came to 181.70 million shares with an hour to go.