NEW YORK (AP) _ The stock market was mixed today, hesitating after reaching record highs in each of the last three sessions.

The Dow Jones average of 30 industrials slipped .78 to 1,336.36 in the first half hour.

Gainers took a 5-4 lead over losers in the early tally of New York Stock Exchange-listed issues.

As the market opened, the Commerce Department reported that new factory orders increased 2.1 percent in May, for their strongest showing in more than six months. Orders declined in both March and April.

Analysts said the figures gave new support to the belief that economic activity was reviving again after a sluggish period early this year.

However, brokers also said some traders found the temptation strong to take profits after the market's recent rise.

Mesa Petroleum led the active list, up 1/8 at 151/8 . The company said it expected to show an after-tax gain from its recent fforts to acquire Unocal Corp.

When Mesa originally agreed to drop its bid for Unocal, the situation was widely considered to be a setback for the company and its chairman, T. Boone Pickens.

Among actively traded blue chips, Sears Roebuck rose 1/8 to 38 ; Texaco was up 1/8 at 371/8 , and American Telephone & Telegraph dropped 1/4 to 24.

On Monday the Dow Jones industrial average recovered from an early loss of about 7 points to close with a 1.68 gain at 1,337.14.

Advances outpaced declines by about 5 to 4 on the NYSE.

Big Board volume totaled 96.08 million shares, against 105.24 million in the previous session.

The NYSE's composite index of all its listed common stocks rose .34 to 111.45. At the American Stock Exchange, the market value index was up 1.01 at 231.90.