J. Walter Thompson Co., one of the world's biggest advertising agencies, announced today that it plans to acquire Hill & Knowlton Inc., the world's largest public relations firm, for $28 million in cash and stock.

Hill & Knowlton -- a privately held company -- will be run as an independent subsidiary of Thompson, the two companies said.

Thompson will reorganize itself, setting up a holding company with the current Thompson operation as a subsidiary and Hill & Knowlton as another. The new parent company will be called JWT Group Inc.

Loet A. Velmans, president of Hill & Knowlton, said the public relations firm needed increased capital resources to undertake the kind of expansion it desired.

"We've got many opportunities to do additional things. But to accomplish them we need a big brother. For example, although we've got 40 offices abroad, there are still a lot more places where we're 'not' than were wer are, "Velmens said.

"If you look at a map, there's a great big blank for Latin America, an area where J. Walter Thompson has had a leading position for many decades," he added.

Velmens said that the public relations firm also wants to make big use of computers and computerization in its research but lacks the capital resources to make the necessary large-scale investment.

"We're big in our field, but really we're a rather small company with $30 million in billings last year," he said.

Thompson -- which was the nation's largest advertising firm until the merger of Young & Rubicam and Marstellar Inc. two years ago -- had worldwide billings of nearly $1.5 billion in 1978. Figures for last year aren't available yet.

Andrew Melnick of Drexel Burnham Lambert Inc. said the proposed merger "meets Thompson's goal of adding new companies under a holding company structure." He said the acquisition, which needs federal approval as well as the approval of Thompson shareholders, will give Thompson a "broader scope."

Thompson will be following the lead of another major advertising company -- Interpublic -- which several years ago adopted a holding-company approach to acquire new subsidiaries.

"I suspect Thompson will have added acquistions, Meinick said.

In the last few years, Thompson has divested itself of a number of businesses that have nothing to do with advertising: a leasing company, a travel company, and a metal electronic company.

J. Walker Thompson already owns a public relations firm. A spokesman for the company said that no decisions have been made about whether to combine its public relations operations with Hill & Knowlton. "Frankly, we haven't gotten down to nuts and bolts. Meetings on the logistics of the merger begin tomorrow (Tuesday)," the spokesman said.

Velmens, president of Hill & Knowlton, said that some of Thompson's public relations operations "might be of interest to Hill & Knowlton." But Velmans said the acquisition agreement will guarantee Hill & Knowlton's independence to assure a complete separation of advertising and public relations.

J. Walter Thompson is publicly held and is traded on the New York Stock Exchange. It closed at $32.25 a share today, down 25 cents from Friday.

Hill & Knowlton, founded 51 years ago, is privately owned by key employes of the advertising agency. Velmans said about 55 of the firm's 800 employes own the 356,000 shares of stock outstanding. These employes have another 58,000 options to buy stock.

J. Walter Thompson said it expects to issue about 395,000 shares of stock in the new holding company and spend about $11.4 million in cash to acquire Hill & Knowlton.