The stock market rallied with renewed force today, pushed by lower interest rates to record highs.

The Dow Jones average of 30 industrials rose 9.63 points to 1,315.41, topping the previous peak of 1,309.70 reached on May 21. For the week, the average gained 13.44 points. Volume on the New York Stock Exchange stepped up to 134.14 million shares from 108.76 million Thursday.

Before the market opened, the Commerce Department reported that new factory orders fell 0.5 percent in April. The drop came after revised declines of 0.7 percent in March and 1.1 percent in February.

However, that fresh evidence of sluggishness in business activity helped touch off a drop in interest rates, and a rise in bond prices, in the credit markets. Prices of long-term government bonds moved up more than $10 for every $1,000 in face value.

The dollar sold off sharply today after the government report on factory orders confirmed a sluggish U.S. economy, UPI reported. The British pound remained on an upward path.

Analysts also said traders were encouraged by the steady showing of International Business Machines' stock despite the company's projection of slightly lower earnings for the second quarter. IBM also said it is still looking for a strong showing in the second half of the year.

As a prominent blue-chip issue and the No. 1 holding of investing institutions, IBM can sometimes set the tone for the market as a whole. After falling a fraction in early trading, it climbed to 128 7/8, up 7/8 from Thursday's close.

Among other actively traded blue chips, American Telephone & Telegraph rose 3/8 to 23 1/4, and Sears Roebuck gained 5/8 to 38 5/8.

Airline stocks were strong, and energy issues mixed, amid talk of new downward pressure on oil prices. UAL, which also got a recommendation from a brokerage house, gained 4 1/4 to 53 5/8; AMR, 2 3/8 to 47 5/8, and Delta, 1 to 48.

The gains in the airline group helped drive the Dow Jones average of 20 transportation stocks up 15.51 points to a new high of 645.16.

On the downside, Black & Decker fell 2 1/8 to 20 1/2. The company said its sales and earnings for the current fiscal quarter will be lower than previously projected.