A senior defense official said Defense Secretary Donald H. Rumsfeld and Poindexter realized that "it would be difficult" for him to continue in his job after the flap over a plan to establish a futures market that would have allowed traders to profit by correctly predicting assassinations and terrorist strikes in the Middle East.

He said Rumsfeld did not ask for his resignation but that Poindexter was "working through the details" and "expects to offer" it within a few weeks.

The project was disclosed Monday by Democratic Sens. Ron Wyden of Oregon and Byron Dorgan of North Dakota. Criticism mounted Tuesday. Senate Armed Services Committee Chairman John Warner, R-Va., later announced he had an agreement from defense officials to end the project.

Warner had spoken by telephone with Tony Tether, head of the Pentagon's Defense Research Projects Agency (DARPA), where Poindexter works. Warner called the program "a rather egregious error of judgment."

DARPA and two private partners would have set up an Internet futures trading market on events in the Middle East. Traders could have bought and sold futures contracts based on their predictions about what would happen in the region. Examples given on the market's Web site included the assassination of Palestinian leader Yasser Arafat and a biological weapons attack on Israel.

Senators had called for Poindexter's resignation.

Sen. Barbara Boxer, D-Calif., said Tuesday that there was "something very sick about it."

"And if it's going to end, I think you ought to end the careers of whoever it was thought that up. Because terrorists knowing they were planning an attack could have bet on the attack and collected a lot of money. It's a sick idea," she said.

DARPA has been criticized by Congress for its Terrorism Information Awareness program, a computerized surveillance program that has raised privacy concerns. Poindexter also is the head of that program.

In the 1980s he was national security adviser to President Reagan. He was a key figure in the 1980s Iran-Contra scandal.