Apple Corps, which contended that the US company had broken a 1991 agreement in which each agreed not to enter into the other’s field of business, said it would appeal.

Judge Edward Mann ruled that Apple Computer used the fruit logo in association with the store, not the music, and thus did not breach the agreement.

‘‘I conclude that the use of the apple logo ... does not suggest a relevant connection with the creative work,’’ Mann said in his written judgment. ‘‘I think that the use of the apple logo is a fair and reasonable use of the mark in connection with the service, which does not go further and unfairly or unreasonably suggest an additional association with the creative works themselves’’.

Neil Aspinall, manager of Apple Corps, said the ruling would be appealed. ‘‘We felt that during the course of the trial we clearly demonstrated just how extensively Apple Computer has broken the agreement,’’ Aspinall said in a statement.

Mann refused Apple Computer’s application for an immediate interim payment of $2.8 million from Apple Corps toward its legal costs, pending further hearings. Apple Corps faces a similar bill for its own legal expenses.

Lawyers for US-based Apple Computer had argued that it was conducting its business legally and that music lovers are smart enough to tell the difference between the logos.

Apple Corps uses a shiny green apple as its logo, while Apple Computer has a cartoon-like apple with a neat bite taken out. Lawyers for each side tussled during the hearing over advertisements for iTunes featuring musical acts U2, Eminem and Coldplay, using the logo.

The 1991 agreement ended previous lengthy litigation over the logo. Apple Computer told the court that it paid the Fab Four’s company $26.5 million as part of the 1991 out-of-court settlement, and in return had received ‘‘a considerably expanded field of use’’.