NEW YORK, JUNE 4 -- The Dow Jones industrial average surged 34 points today to yet another record close, driven by flurries of computerized program trading, the prospect of lower interest rates and momentum left over from last week's 80-point advance.

A modest morning rally broadened in the last two hours of trading as more than 1,000 New York Stock Exchange issues posted advances on the Big Board, compared with 462 declines.

Some broad blue-chip stock indexes also posted new record highs along with the Dow -- the NYSE Composite, for example, consisting of approximately 1,700 issues traded on the Big Board.

Shortly after 2 p.m., the first of four waves of index-arbitrage buy-programs locked in. Trend-following day-traders hopped on the bandwagon as the Dow pierced morning resistance near 2907, and some institutional managers stepped up their methodical buying in targeted stocks amid fear of a runaway market, block traders said.

"This market is strong and getting stronger," said Jon Groveman, president and chief trader at Ladenburg, Thalmann.

At the close, the Dow stood at 2935.19, up 34.22. Trading was moderately active of 175 million shares.

Among Dow components, Chevron finished up 7/8 at 70 3/8, partially on publicity surrounding its negotiations with the Soviet Union in regard to joint development of the U.S.S.R.'s huge Tengiz oil field.

But Chevron was outstripped by other Dow movers. Philip Morris rose 1 1/4 to 44 1/2, Minnesota Mining gained 1 3/4 to 85, Alcoa added 1 1/2 to 68 1/4, American Express moved up 1 7/8 to 31 5/8, Boeing advanced 1 5/8 to 86 3/8 and Coca-Cola tacked on 1 1/4 to 46 1/2.

L.A. Gear topped the NYSE most-active list with 3.1 million shares. Gear recovered from a loss of more than 1 1/2 points at midday to close down only 1/8 at 30 5/8 in the wake of last week's 18 3/8-point price debacle tied to a slash in the company's May 31-quarter earnings estimate.

Geico Inc. climbed 1 1/2 to 156 1/2, a high for the year. Geico has had talks with the French insurer Axa-Midi Assurances concerning the possible acquisition of some or all of Geico by Axa, sources said.

The talks, however, were described as very preliminary. "No action has been taken," and the companies are "nowhere near a decision," according to one source close to the situation. Axa-Midi has been in the market for a U.S. insurer, but a plan to acquire California-based Farmers Group was rejected by state regulators in April.

Utility, finance and insurance stocks benefited from a slight drop in interest rates confirmed in a Treasury bill auction today. Among them: Washington-based Federal National Mortgage Association, up 1 7/8 to 43 5/8.

Also actively traded was money-center bank First Interstate, which rose 4 7/8 to 44 7/8, a 14 percent advance, on 1.9 million NYSE shares. Some of First Interstate's volume was attributed to dividend-capturing tactics -- the stock went ex-dividend today -- but much was said to arise from resurgent rumors about a potential takeover by either Wells Fargo or Security Pacific. Wells Fargo rose 3 5/8 to 84 1/2 today, while Security Pacific gained 1 7/8 to 42 1/4 amid a generally strong banking sector.

Retailer Wal-Mart added 2 1/4 to 60 1/2 following Friday's announcement by Chairman Sam Walton that he expects to double the number of stores in the next decade.

The Dow transports finished up 17.70 at 1207.85, while the utilities surged 3.71 to 215.42.

Among broad stock indexes, the Standard & Poor's 500 was up 4.24 at 367.40, a new record high, while the Value Line was up 2.33 at 290.69, the Amex Market Value up 0.57 at 364.40 and the Nasdaq Composite up 3.48 at 465.61.