Book publisher Prentice-Hall Inc., which three weeks ago balked at a takeover proposal from Gulf & Western Industries Inc., yesterday agreed to a new offer from G&W worth $1 a share more.

Prentice-Hall's board, which had unanimously rejected the original offer of $70 a share as "inadequate" and put into place a number of defenses against a hostile takeover while it apparently waited for a competing bid that never came, also voted unanimously in favor of the new $71-a-share bid from Gulf & Western. The total value of the new bid is $710 million.

Stock in Prentice-Hall, which had been buoyed by stock market speculation over a possible competing bid, fell 50 cents to $70.75 a share on the American Stock Exchange.

The acquisition of Prentice-Hall would make Gulf & Western, which already owns Simon & Schuster and several other publishing firms, one of the biggest book and software publishers in the nation. Last week, the Justice Department said it would not contest the proposed merger on antitrust grounds.

Gulf & Western had continued its pursuit of Prentice-Hall in spite of that company's opposition, and though it is not known how many Prentice-Hall shares have already been tendered, or promised, to G&W at the lower price, the company said it would pay $71 a share for all of Prentice-Hall's stock. The offer is to expire Dec. 10.

Under the merger agreement, Prentice-Hall's management will remain in place after the takeover.

"We are delighted that we have reached an agreement with Gulf & Western," Prentice-Hall President Donald A. Schaefer said. "The combined financial and human resources resulting from the merger will enable both companies to accelerate growth in our respective markets."

"We are extremely pleased that a merger agreement has been worked out," said G&W Chairman Martin S. Davis.