NEW YORK, JUNE 23 -- The stock market declined in active trading today, snapping an 11-day advance as the support it had drawn from the stronger dollar and bond markets began to fall away.

The Dow Jones average of 30 industrials fell 5.78 points to 2439.73.

Declines outpaced advances by about 3 to 2 on the New York Stock Exchange.

Big Board volume totaled 194.20 million shares, up from 178.21 million Monday.

The market started out by posting a strong gain. The closely watched Dow Jones barometer had advanced a brisk 10.17 points by 11 a.m. at 2455.68.

But stock prices began to sag around midday, as the dollar dropped and bond prices fell.

"The stock market took its cue from those two {bonds and the dollar}," said Hugh Johnson, senior vice president at First Albany Corp., a brokerage firm in Albany, N.Y.

Analysts suggested that Wall Street's new bearish sentiment could have been deepened by today's news that the United States owed the rest of the world $263.6 billion at the end of 1986, lengthening its lead as the world's largest debtor nation.

Shares of Dayton Hudson Corp. gyrated wildly after a Cincinnati portfolio manager made a purported $70-a-share buyout offer for the company. The offer was later discredited. The retailer has been the target of takeover speculation for weeks. It closed at 53, down 1, and was the second most actively traded stock on the NYSE.

The government said today that consumer prices edged up 0.3 percent in May, the smallest increase this year, and that new orders for "big ticket" durable goods in May slipped 0.1 percent in the first decline in four months. But neither report had much impact on stock prices, observers said.

Among other actively traded issues, AT&T declined 1/8 to 28 1/2, IBM advanced 1 3/4 to 165, Commonwealth Edison lost 1/8 at 36 1/4, Gillette fell 3/8 to 38 7/8, General Electric was down 1/2 at 55 and K mart rose 7/8 to 44 5/8.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 226.40 million shares.

The NYSE's composite index was down 0.55, at 173.22.