The Pentagon office that proposed spying electronically on Americans to monitor potential terrorists has a new experiment. It is an online futures trading market, disclosed today by critics, in which anonymous speculators would bet on forecasting terrorist attacks, assassinations and coups.

Traders bullish on a biological attack on Israel or bearish on the chances of a North Korean missile strike would have the opportunity to bet on the likelihood of such events on a new Internet site established by the Defense Advanced Research Projects Agency.

The Pentagon called its latest idea a new way of predicting events and part of its search for the ''broadest possible set of new ways to prevent terrorist attacks.'' Two Democratic senators who reported the plan called it morally repugnant and grotesque. The senators said the program fell under the control of Adm. John M. Poindexter, President Ronald Reagan's national security adviser.

One of the two senators, Byron L. Dorgan of North Dakota, said the idea seemed so preposterous that he had trouble persuading people it was not a hoax. ''Can you imagine,'' Mr. Dorgan asked, ''if another country set up a betting parlor so that people could go in -- and is sponsored by the government itself -- people could go in and bet on the assassination of an American political figure?''