NEW YORK, JUNE 4 -- A late round of buying carried stock prices higher today, adding to Wednesday's strong gains.

The pace of trading remained sluggish, however.

The Dow Jones industrial average rose 16.39 to 2337.08. It had risen 42.47 points on Wednesday.

Volume on the New York Stock Exchange was 140.30 million shares, down from 164.17 million in the previous session.

Analysts generally were pleased that the securities markets quickly stabilized Wednesday after the jolt of Tuesday's news that Paul A. Volcker would be stepping down as chairman of the Federal Reserve Board.

Stocks and bonds benefited from widespread praise for Alan Greenspan, the man picked as Volcker's successor. Many Wall Streeters spoke of Greenspan as a "Volcker clone" on policy matters.

But observers weren't totally impressed by the advance in stock prices Wednesday and today, noting that it lacked the kind of trading volume that would suggest broad-based enthusiasm.

They said some investors apparently were inclined to remain cautious pending next week's economic summit meeting in Venice.

Before that, the next item on the agenda for investors is Friday's report on employment.

Waste Management led the active list, down 2 1/8 at 40 1/4 on a Wall Street Journal report of a federal antitrust investigation into practices in the waste disposal industry.

Gainers among the blue chips included International Business Machines, up 1 1/8 at 161 3/8; Merck, up 7/8 at 160 1/8; Du Pont, up 2 1/4 at 116; Eastman Kodak, up 3/4 at 79 3/4, and Minnesota Mining & Manufacturing, up 3/4 at 130 1/4.

British stocks lost ground amid uncertainty about approaching elections there. Barclays fell 1 7/8 to 34 1/2, National Westminster 1 1/8 to 32 5/8, British Telecom 1 1/4 to 51 3/4 and British Gas 7/8 to 29 1/8.

Leading Japanese stocks moved up. Hitachi gained 3 to 77 1/4; Honda Motor 5 5/8 to 104 1/4 and Matsushita Electrical 2 1/4 to 132 3/4.