A tobacco-industry trade association and an anti-tobacco health coalition have formed an unusual alliance with federal legislators to seek passage of a compromise bill to require strong health warnings on packages and print advertisements for smokeless tobacco.

The measure also would ban television and radio ads for smokeless tobacco products -- chewing tobacco and snuff -- some of which have been promoted by athletes and entertainers. Congress banned broadcast ads for cigarettes in 1970 and for little cigars in 1973.

The draft warnings would say, in capital letters, "This product may cause oral cancer," "This product may cause gum disease and tooth loss," and "This product is not a safe alternative to cigarettes." The warnings would rotate, as do those for cigarettes.

Smokeless tobacco is consumed in the mouth and -- unlike cigarettes -- neither is burned nor exhaled. An estimated 22 million Americans use it, according to the National Cancer Institute. The most popular among some 165 brands are moist snuff, but also include dry snuff and plug and chewing tobacco.

The compromise legislation was fashioned after months of negotiations involving the Smokeless Tobacco Council, an industry trade group, and the Coalition on Smoking and Health -- whose primary members are the American Heart Association, American Lung Association and American Cancer Society.

Rep. Henry A. Waxman (D-Calif.), who had cosponsored a stiffer measure, asked for unanimous consent to enable the House to act on the compromise Dec. 19, but was blocked by one objection, from Rep. Thomas J. Bliley Jr. (R-Va.). Bliley, whose district includes 10,000 employes of Philip Morris Inc., said he feared the tougher warnings could be required later for cigarettes.

Backers of the compromise expect it to pass both houses with little difficulty in the new session of Congress.

Michael J. Kerrigan, president of the Smokeless Tobacco Council, said the spur to work out the compromise with the Coalition on Smoking and Health and other adversaries was the recognition that only uniform, if "very distasteful," federal legislation could head off adoption by numerous states of "conflicting and differing warning statements."

The compromise dropped a proposed federal warning that nicotine is addictive, which had been in the measure sponsored by Waxman, chairman of the House Energy and Commerce health subcommittee, and Rep. Michael L. Synar (D-Okla.). The tobacco industry vehemently denies that scientific evidence shows either smokeless tobacco or cigarettes to be addictive.

The version that passed the Senate last month, on the other hand, did not ban TV and radio commercials for smokeless tobacco.

The compromise measure also would draw attention to the word "WARNING" by enclosing it in a fat arrow that pierces a circle and points to the text inside the circle. The intent was to make them more conspicuous than the warnings on cigarette packs and in cigarette ads.

The Tobacco Institute, the cigarette manufacturers' trade association, was not involved in the compromise process. Sales of smokeless tobacco products total about $1 billion a year compared with $21 billion for cigarette sales.

Lawyers said the legislation would make it difficult for a user to blame a disease on smokeless tobacco that carried a warning label. But the measure, which would require the warnings and ban commercials six months after enactment, would not affect product liability suits by persons who used the products earlier.

Two product liability suits are pending, both against United States Tobacco Co. of Greenwich, Conn., which makes the biggest-selling brands of moist snuff in the world, Copenhagen and Skoal. The company's U.S. sales of moist snuff totaled $380 million in 1984, a 15.7 percent increase over the year-earlier results.

The U.S. surgeon general has said that smokeless tobacco is richer in certain cancer-causing toxins than any other consumer product taken by mouth. The Senate committee report on its bill cited a study indicating that chronic long-term users of smokeless tobacco run a cancer risk nearly 50 times greater than non-users.

But the industry's Kerrigan told a Waxman subcommittee hearing last July that "it has not been scientifically established that smokeless tobacco is the cause of any human disease."