''We finally wore Steven Spielberg down,'' said Gene Giaquinto, president of M.C.A. Home Entertainment, in explaining why ''E.T. the Extra-Terrestrial'' is to be released on video cassette in October.

There has been, in Mr. Spielberg's words, ''a war'' to make him agree to put his 1982 film, the top box-office movie of all time, on cassette. Marvin Levy, a spokesman for Mr. Spielberg, who is in Spain directing his third ''Raiders of the Lost Ark'' movie, said: ''Steven told me: 'Since 1982, I've been inundated with three questions: When is ''E. T.'' coming to home video? Will there be a sequel? And what is Michael Jackson really like?' Steven was finally worn down by the world.''

The cassette of ''E.T.'' is to go on sale worldwide on Oct. 27 for $24.95. A $5 rebate from Pepsi-Cola will reduce the price still further, to $19.95. So far, ''Top Gun'' has had the lowest original release price of any major film. With a Diet Pepsi commercial attached to the movie, ''Top Gun'' was released at $26.95 and sold 2.9 million cassettes. ''E.T.'' will not carry a commercial. E.T. in Pepsi Commercials

Pepsi-Cola approached M.C.A. almost a year ago, and the two companies have been working out the details ever since. M.C.A. said the rebate, which reduces the price to less than $20, allowed Mr. Spielberg to feel secure that most people will have access to carefully crafted cassettes rather than cheap low-quality pirated copies. Pepsi is also going to make commercials featuring the character of E.T.