In his long-standing, and sometimes torturous, effort to gain control of

Nabisco Group Holdings

(NGH)

, corporate raider Carl Icahn outlined a new scenario for the shares of the company he doesn't already own, saying he is prepared to offer $6.5 billion in cash and notes, or $22 a share.

That is a premium of 38% to the $16 a share he

offered at the beginning of April, with the new bid comprised of a $19-per-share cash component and a two-year note valued at $3. Icahn described his potential offer in a letter Thursday to the Nabisco Group; the letter was included in a Schedule 13D filed with the

Securities and Exchange Commission

.

Nabisco Group holds an 80.6% stake in

Nabisco Holdings

(NA)

, the maker of products such as Oreo cookies and Planters peanuts. Last month, Nabisco Group said it was exploring a sale of either the entire Nabisco Group or its stake in the subsidiary. Both are based in New York.

The news comes a week after speculation that

R.J. Reynolds Tobacco Holdings

(RJR)

might make a

bid for its former parent. R.J. Reynolds and Nabisco have led intertwined corporate lives since 1985, when the tobacco company first bought the food company. The maker of such cigarettes as Winston and Camel, spun off last year, might take an interest in the holding company if it first gets a decent price for its stake in Nabisco, according to a theory floated by Martin Feldman,

Salomon Smith Barney's

tobacco analyst.

This is Icahn's fourth attempt since 1995 to buy Nabisco and follows a proposal on March 13 to take over the company's board. After Icahn made his intentions known, Nabisco adopted a shareholder rights plan, or "poison pill," which aims to discourage takeovers by granting current shareholders the right to buy preferred stock if any person gains control of 10% of the company's ownership. Icahn and his affiliates currently own 31.2 million shares, or a 9.6% stake.

Shares of Nabisco Group rose 1 3/4, or 10%, to 19 5/16 in midday Friday trading, while shares of Nabisco Holdings rose 3/16 to 43 3/4. (Nabisco Group Holdings closed up 2 1/8, or 12%, at 19 11/16, while Nabisco Holdings finished up 3/8, or 1%, at 43 15/16.) Shares of R.J. Reynolds were up 1, or 5%, to 22 5/8. (R.J. Reynolds closed 1 9/16, or 7%, at 23 3/16.)