The Washington Post Co. said yesterday it has agreed to acquire 17 percent of Cowles Media Co., publisher of the Minneapolis Star and Tribune newspaper, from dissident Cowles stockholder Kingsley H. Murphy Jr.

Terms of the transaction were not disclosed. The thinly traded Cowles Media stock jumped $40 a share yesterday, with a block in excess of 10,000 shares changing hands at $120 a share, according to Gordon Bowles, a stockbroker with Piper Jaffray & Hopwood.

At that price, the cost to The Post Co. would have been about $64 million.

According to documents filed in a lawsuit by Murphy's family against Cowles Media, Kingsley Murphy said The Post made a preliminary offer in early January to buy his family's shares for about $45 million to $60 million, or $85 to $113 a share.

A spokesman for The Post Co. said yesterday the purchase of Murphy's stock was for investment purposes only. Securities industry experts said they believe The Post Co. purchased the 17 percent block with the hope that it might be able to acquire the rest of Cowles Media at some point in the future.

While about half of Cowles Media stock is held in a trust and the company repeatedly has said it is not for sale, speculation that it might be sold has increased recently. The Cowles family decided in December to sell another company it controls, The Des Moines Register and Tribune Co., after making similar statements that it was not for sale.

Gannett Co. Inc., publisher of USA Today and the nation's largest newspaper chain, was the winning bidder for The Register Co.'s newspaper operations, with an aggressive $200 million offer.

The announcement by The Post Co. yesterday came just one day before First Boston Corp., The Register Co.'s investment banker, is to receive preliminary bids from parties interested in buying a 14.3 percent block of Cowles Media stock owned by The Register. The Cowles Media stock was not part of the Gannett purchase.

The Register Co. is trying to decide, as it moves ahead with its liquidation, whether to sell the stock to a single party or distribute it broadly to Register stockholders.

Register Chairman David Kruidenier, who also is chairman of Cowles Media, said yesterday he hopes a decision on what to do with the 14.3 percent block will be made by March 25, when The Register Co.'s directors meet.

Several securities industry experts said they believe The Post will bid aggressively for the 14.3 percent block, because a winning bid would give it a 31 percent stake in Cowles Media. "If they end up with 31 percent, I'd be surprised if they didn't end up with the whole thing eventually," said one Wall Street expert.

Kruidenier issued the following statement to Cowles employes in Minneapolis yesterday:

"We have learned this morning that The Washington Post Co. has agreed to purchase the 17.1 percent interest in Cowles Media Co. held by Kingsley H. Murphy Jr. and his family. Financial details of the transaction were not disclosed.

"This purchase in no way changes the position of the voting trust [owners of more than 50 percent of Cowles Media voting shares]: The company has not been for sale and is not for sale now. While we have had no discussions with The Post about their purchase, we are sure that they understand our position about the future of Cowles Media.

"The stock owned by the Murphy family has been for sale for a number of months. We are glad to have the matter resolved and are delighted that a company of the stature of The Post wants to make this long-term investment in this company."

Kruidenier also said yesterday that an announcement Feb. 26 by Cowles Media that it plans to invest about $110 million in a new satellite plant and presses can be regarded as symbolic of the company's plans to remain under current ownership.

In addition to the Minneapolis Star and Tribune newspaper, which has a circulation of 372,000, Cowles Media owns the Rapid City Journal in South Dakota, the Great Falls Tribune in Montana, the South Idaho Press in Burley; a group of suburban newspapers in Denver, and a commercial and directory printing business.