NEW YORK, OCT. 8 -- The Dow Jones industrial average trimmed an early 34-point gain to only 13 points today in thin, Columbus Day trading.

An initial rally swept the index as high as 2544, the result of strong stock markets overseas and initial index-arbitrage program buying, but prices began to slip in midmorning. The Dow fell to a 5-point advance in early afternoon after slowly rising oil prices topped $39 a barrel. As has often occurred in recent weeks, spurts in oil prices produced inverse reactions in the stock market.

A sharp new decline in long-suffering takeover candidate UAL Corp. also helped dampen the tone of trading, as did continued longer-term concern over the ability of an ideologically divided Congress to tackle the problem of runaway federal budget deficits. Although the House approved a modified budget resolution in the wee hours of the morning, a Senate vote still loomed by the time stocks closed.

At the close, the Dow stood at 2523.76, up 13.12, while advancing issues outpaced declining ones on the Big Board by a 4-to-3 ratio on light holiday volume of 99.8 million shares -- the third-lightest trading day of the year -- compared with a moderate 153-million pace on Friday.

Among Dow components, moves were generally fractional all day. Exceptions were Procter & Gamble, which gained a full point to 80 1/8 into the close, and IBM, which extended an early advance to 1 1/4 at 109 1/2. General Motors, which faces a strike deadline from 36,000 Canadian workers on Wednesday and unveils its new Saturn line on Thursday, edged up 5/8 to 37 1/2.

Among industry groups, many food and drug stocks moved moderately higher, as did integrated petroleum companies. But insurance stocks suffered from carry-over selling after Friday's broad declines, when Travelers announced a dividend cut and a big addition to loan-loss reserves to cover real estate exposure.

Among the battered diversified insurance stocks, Travelers itself closed down 2 to 14 3/8 after its hefty 5 1/8 loss last week, while Aetna trimmed a 3-point early loss to finish down 1 5/8 at 32 and Marsh and McLennan lost 1 3/8 to 63 7/8. Continental Corp. gave up 1 to 18 3/8, but many of the property and casualty insurers that lost ground on Friday bounced back fractionally on light bargain hunting today.

Among stocks in the news, UAL Corp. tumbled 11 1/2 to close at 91 1/4, only 1 3/8 above its dismal opening level. Other airline stocks were not particularly affected, however, although the loss dragged the Dow transportation index down 6.66 to 859.66.

The Dow utilities, however, surged 3.08 to 208.50, convincing some traders that prospects are brightening for easing interest rates, whether through Federal Reserve action or simply because an increasingly sluggish economy will eventually smother loan demand.

Among broad stock indexes, the Standard & Poor's 500 was up 1.98 at 313.48, the NYSE Composite up 0.95 at 171.65, the Value Line up 0.48 at 229.60, the Amex Market Value up 0.03 at 306.51 and the Nasdaq Composite up 0.78 at 348.14.