Storer Communications Inc., the Miami-based media company fighting a dissident shareholder group, announced a partial buyout plan yesterday in which $100 a share in cash and securities will be offered for up to 6 million shares of the company's common stock.

The announcement of the recapitalization was made late yesterday, following a long meeting of the company's directors. Storer stock, which opened late for trading on the New York Stock Exchange yesterday, closed at 76 1/4, up 1 3/8.

Storer has about 16.4 million shares outstanding.

Storer also said its board received and turned down a leveraged buyout proposal of $75 in cash and $25 in securities per share from New York-based Kohlberg, Kravis Roberts & Co. Storer said that it would have been obliged under KKR's proposal to pay the firm $3 million for preparing and submitting the offer.

Storer recently became the first media company to be the target of a hostile takeover bid. A dissident shareholder group has proposed its own slate of directors for election at the company's annual meeting next month, along with a plan to maximize the return to shareholders by liquidating the company.

Thursday, CBS Inc. became the second media company to be the target of a hostile takeover bid when broadcaster Ted Turner launched a $3 billion bid for the company. Even though Turner's bid may not succeed, CBS may be forced to take steps, as Storer did yesterday, to enhance the value of its shares.

Storer operates cable television systems in 18 states and owns seven television stations. The company proposed the recapitalization yesterday, according to some Wall Street investment bankers, after it appeared that it might lose the proxy fight next month, and after the Federal Communications Commission decided not to intervene in the hostile takeover attempt.

Storer's recapitalization plan approved yesterday will be implemented in steps. In the first step, the company will exchange $40 a share in cash and $60 in face amount of a new issue of subordinated debt for each of up to 3 million shares of common stock. That exchange offer is expected to begin next week.

Storer also will offer the same terms for another 3 million shares in the second stage of the recapitalization. However, that will not begin until after the company sells certain assets, which it did not identify, and retires certain outstanding debentures.

Storer has lost money for the last several years, following heavy investment in cable television, but is expected to make a profit this year.

"The offer provides those shareholders wishing to dispose of shares at this time the opportunity to receive cash and a debt security of the company," the company's president, Peter Storer, said. "Alternatively, shareholders can retain their stock and share in the company's future."

Storer said directors of the company, who own about 423,000 Storer common shares, do not intend to tender their shares. He recently said the dissident shareholder group's announcement that it could give shareholders between $90 and $100 a share in value by liquidating the company is overstated by about $30 a share, and said that by 1987, Storer stock could be worth $200 a share if current management remains in control.

"We intend to continue to solicit proxies for our slate of directors," said Augustus Oliver, a member of the dissident shareholders group. "Our preliminary reaction is the recapitalization is inadequate."

The securities Storer plans to exchange for common stock will pay no interest for three years from the day of issue and then will pay 16 percent per year. They will mature in 10 years.