The publication of a book here today by an American historian declaring that the Holocaust has become an ''extortion racket'' through which some Jews blackmail Germany has ignited a stormy debate.

A television documentary on the author, Norman Finkelstein, that was to have been carried on Monday was canceled at the last moment, and newspapers have been full of virulent discussion over whether the book is a ''breath of fresh air,'' as one has put it, or a dangerous invitation to anti-Semitism.

''Germany is right to reject the use of the Nazi Holocaust as a weapon for political and economic gain,'' Mr. Finkelstein said at a packed news conference. ''The Holocaust has long since ceased to be a source of moral and historical enlightenment. It has become a straight-out extortion racket.''

The author, whose parents were Holocaust survivors, was presenting the German translation of his book, ''The Holocaust Industry'' (Verso), published last year in the United States to a generally hostile reception. It was also published in Britain. Its central argument is that what he calls an ''American-Jewish elite'' has appropriated the Holocaust and debased it for financial gain.