NEW YORK, JUNE 1 -- The stock market showed no clear trend today in a cautious response to new signs of a stabilizing dollar and falling interest rates.

The Dow Jones industrial average, up more than 10 points at one point, closed with a 3.34 point loss at 2288.23.

Volume on the New York Stock Exchange came to 149.34 million shares, down from 153.50 million in the previous session.

Analysts said the currency and credit markets have generally worked in the market's favor lately.

With the dollar having steadied against leading foreign currencies of late, interest rates have turned downward, halting a rise that began in early spring.

Prices of long-term government bonds, which move in the opposite direction from interest rates, today managed some modest gains.

Another apparent plus for the markets was a Wall Street Journal report that Paul A. Volcker is likely to be reappointed as chairman of the Federal Reserve after his current term expires in August, provided that he wants to continue in the job.

However, the White House has made no official decision, and the possibility remains that Volcker might not want to serve a third four-year term.

Wall Streeters generally hold Volcker in high regard and fear that a change of leadership at the central bank might lead to at least a short period of turbulence in the markets.

Analysts also noted that trading volume has been sluggish lately, suggesting a persistent mood of uncertainty among market participants.

Losers among the blue chips included Du Pont, down 1 1/2 at 111 1/4; Eastman Kodak, down 1 5/8 at 78 1/8; International Business Machines, down 3/8 at 159 5/8, and General Electric, 5/8 lower at 51 3/8.

Uccel, which agreed to be acquired by Computer Associates in an exchange of stock, jumped 11 5/8 to 43 5/8, posting the day's biggest percentage gain among NYSE issues. Computer Associates slipped 7/8 to 27 1/8.

Hospital Corp. of America rose 1 1/4 to 48. The company approved a plan to sell more than 100 general hospitals to an employe group.

Circus Circus Enterprises picked up 1 3/8 to 26 7/8. The company reported that its earnings for the fiscal quarter ended April 30 came to 37 cents a share, up from 23 cents in the comparable period a year earlier.

Advancing issues outnumbered declines by about 9 to 8 on the NYSE. The exchange's composite index closed at 163.48, unchanged from Friday.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 173.88 million shares. Standard & Poor's index of 400 industrials fell 0.49 to 336.35, and S&P's 500-stock composite index was down 0.27 at 289.83.