NEW YORK, FEB. 5 -- The stock market drifted through another sluggish session today, drawing practically no benefit from a renewed decline in interest rates.

The Dow Jones average of 30 industrials fell 13.09 to 1910.48, extending its loss for the week to 47.74 points. Advancing issues slightly outnumbered declines among New York Stock Exchange-listed issues.

Big Board volume came to 161.31 million shares, down from 186.49 million in the previous session.

The bond market staged a strong advance in response to the Labor Department's report of a smaller-than-expected increase of 107,000 in nonfarm payroll employment for January. Prices of long-term government bonds jumped about $15 for each $1,000 in face value, putting their yields as low as 8.3 percent. The relatively small employment increase was taken as a sign that the economy started 1988 on a subdued note, suggesting the Federal Reserve might find room to ease its credit policy.

Auto stocks were a notable weak spot in today's trading. Chrysler, which said it would incur large startup costs for new models in the current quarter, dropped 1 7/8 to 24 1/8; General Motors fell 1 1/8 to 63 1/8, and Ford Motor dropped 1 3/8 to 40 7/8.

Elsewhere among the blue chips, International Business Machines lost 5/8 to 108; American Telephone & Telegraph 1 1/8 to 28 3/4, and General Electric 1 to 42 1/2.