NEW YORK, SEPT. 30 -- The stock market eked out a small gain today, thanks to a modest round of buying near the close.

The Dow Jones average of 30 industrials, which had dropped 10.93 points on Tuesday, rose 5.71 to 2596.28. Volume on the New York Stock Exchange came to 183.07 million shares, up from 173.53 million in the previous session.

Analysts said fluctuations in interest rates continued to set the tone for the market.

After climbing on Tuesday to their highest levels in almost two years, surpassing 9 3/4 percent, rates on long-term Treasury bonds dropped back a bit today. But analysts said stock traders remained worried that rates might be subjected to more upward pressure soon.

Meanwhile, the dollar rose slightly against key currencies as traders settled their accounts at the end of the third quarter.

The dollar advanced against the yen in Tokyo for a seventh straight session, closing at 146.35 Japanese yen, up from 146.05 yen late Tuesday. In later London trading, the dollar edged up to 146.45 yen. In New York, the dollar rose to 146.60 yen from 146.565 yen late Tuesday.

The Dow Jones industrial average finished September with a net loss of 66.67 points.

Among actively traded blue chips today, Ford Motor rose 1 3/4 to 97 5/8; International Business Machines was up 1/4 at 150 3/4; General Electric gained 1/4 to 61 1/2, and American Telephone & Telegraph fell 5/8 to 33 3/4.

Bear Stearns gained 1/4 to 20. The company reached an agreement for Jardine Strategic Holdings Ltd. of Hong Kong to acquire about a 20 percent stake in it for $23 a share.

Among other leading investment banking and financial services stocks, First Boston rose 1 to 45; Morgan Stanley 1 to 80 7/8; Merrill Lynch 1/8 to 38 1/8, and American Express 1/4 to 35 7/8. Salomon Inc., which is getting a large investment from Berkshire Hathaway Corp., slipped 1/2 to 36 3/8 after climbing 2 1/8 Tuesday.

Santa Fe Southern Pacific led the active list, up 4 3/4 at 63 5/8 in buying spurred by takeover rumors.

Advancing issues outnumbered declines by about 4 to 3 on the Big Board. The exchange's composite index of all its listed common stocks added 0.18 to 180.24.