The Dow Jones industrial average scored its third straight record close Friday as a strong bond rally, fueled by a bullish employment report, helped stocks close moderately higher in heavy trading.

The Dow, which rose 5.06 points Thursday to close above 3800 for the first time ever, climbed another 16.89 points Friday to 3820.77.The New York Stock Exchange composite index also rose 1.34 to 260.34, while Standard & Poor's 500-stock index climbed 2.78 to 469.90. The price of an average share gained 18 cents.

Advances topped declines 1,219-843 among the 2,695 issues crossing the NYSE tape.

Adjusted volume slid to 323,366,000 shares from 363,448,000 in the same period Thursday, but it was the fourth time in a row that volume topped 300 million.

Prices ended slightly higher on the American Stock Exchange and the Nasdaq Stock Market.

The Amex Market Value Index added 0.49 to 479.49 for its 12th consecutive climb, moving within striking distance of its record-high close of 484.28 set Nov. 12.

Treasury securities climbed to session highs, while the U.S. dollar remained slightly lower.

In overseas trading, the Tokyo stock market climbed for the third straight day, London gained more ground and Paris rallied to record heights. Frankfurt, however, extended its decline to a fourth day.

Paris' blue-chip CAC40 Index jumped another 32.49 points to 2,307.55 - topping Monday's record-high close of 2,290.56.

On Wall Street, Philip Roth, chief technical analyst at Dean Witter Reynolds Inc., said stocks got "a big help from the bond market."

He said the strong bond rally "enabled financial and utilities issues to rebound. They've been performing poorly this week."

Although stocks also benefited from the so-called January effect - the traditional start-of-the-year reinvestment - such activity was marked by "a great deal of group rotation," Roth said.

Hildegard Zagorski, vice president for national sales at Prudential Securities Inc., said the market dipped briefly in morning trading as it "ran into a bit of profit taking, which was not unusual" after two straight record closes.

Zagorski said she felt encouraged by the fact that the Dow utilities average was up Friday fol-lowing Thursday's 1.26 percent drop. Thursday also marked its seventh straight decline.

Analysts said Wall Street opened modestly higher as the market again drew encourgement from another bond rally following a weaker-than-expected report on December employment.

But they said the market would likely attract more profit taking with the Dow hovering over 3800.

The blue-chip indicator broke the 3800 barrier Thursday for the first time as it set its second straight record close, although stocks finished mixed overall as profit taking chipped away at early gains fueled by a bond rally.

On the NYSE trading floor, Blockbuster Entertainment paced the Big Board actives, losing 15/8 to 281/4. The Wall Street Journal said Blockbuster and Viacom were negotiating a merger aimed at enabling Viacom to outbid QVC Network in the battle for Paramount Communications.

Paramount rose 3/4 to 791/4 on the Big Board, while Viacom Class A fell 7/8 to 461/8 on the Amex and QVC gained 11/8 to 405/8 on the Nasdaq.

Circuit City Stores was the second most active, edging up 1/8 to 173/4. Its shares had been down most of the day after a rating downgrade from Piper Jaffray Inc. Circuit City's shares skidded Thursday after the company said reductions in gross profit margins and increased costs related to its expansion program would result in flat earnings growth in fiscal 1995.

Telefonos de Mexico was third, falling 7/8 to 667/8.

On the Amex, the average price of a share added 1 cent. Advances led declines 324-257 among the 836 issues traded. Volume eased to 21,468,000 shares from 22,487,000 traded Thursday.

Calton led the Amex actives, rising 7/16 to 21/2.

The Nasdaq composite index rose 2.53 to 782.94. Advances edged declines 1,248-1,024 among the 3,363 issues traded.

MCI Communications led the Nasdaq actives, falling 7/8 to 273/8.