NEW YORK, JUNE 9 -- The stock market inched higher in moderate, lackluster trading today, showing little conviction in its rise after seesawing narrowly through most of the session.

The Dow Jones average of 30 industrials edged up 1.06 points to close at 2352.70. Advancing issues outnumbered decliners by about 8 to 7 on the New York Stock Exchange. Big Board volume totaled 164.18 million shares, up from 136.37 million in Monday's light session.

Analysts said stock prices were dampened by a fall in the dollar on world currency markets and weakness in bond prices.

"I think {stock market traders} are really focusing on the dollar," said Michael Metz, an analyst for Oppenheimer & Co. However, he added, Wall Street would have been expected to retrench somewhat following its brisk gains late last week and on Monday.

Market participants are watching for news from the economic summit of seven major industrial countries in Venice, although many traders don't expect significant developments to emerge from the conference, which ends Wednesday.

The finance ministers today reaffirmed their February agreement to cooperate closely to stabilize exchange rates, but the action was unsurprising and failed to impress the market.

"We've got the Venice serenade going on," said Richard Schmidt, vice president and research director for Advest Inc. in Hartford, Conn. "I don't think there's going to be much going on here until we see some results of this {summit}."

A communique to be issued at the end of the Venice summit was expected to contain a pledge by the seven governments to take unspecified necessary measures if economic growth doesn't meet expectations.

Wall Street also was looking toward the U.S. trade deficit figures for April, to be released by the Commerce Department on Friday. The Reagan administration has been hoping that the dollar's fall, by making U.S. goods more attractive abroad, would carve a substantial dent in the nation's massive trade deficit. The monthly trade gap was $13.6 billion in March.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 191.37 million shares. The NYSE index was up 0.25, at 167.38.

Standard & Poor's index of 400 industrials edged up 0.80 to 344.99, and S&P's 500-stock composite index was up 0.56 at 297.28.

At the American Stock Exchange, the market value index rose 1.17 to 331.53. The Nasdaq composite index for the over-the-counter market closed at 421.67, up 2.26.

Airline issues were strong, boosted by fare increases linked to fuel prices by several major carriers. AMR rose 1 1/4 to 59 3/8, Allegis advanced 1 1/4 to 90 3/4, NWA was up 1 1/8 at 71 1/4, Pan Am gained 3/8 at 5 3/8, Piedmont was up 1/8 at 68 3/4 and USAir rose 1 5/8 to 45 5/8.