The Pentagon is constructing a computer system that could create a vast electronic dragnet, searching for personal information as part of the hunt for terrorists around the globe -- including the United States.

As the director of the effort, Vice Adm. John M. Poindexter, has described the system in Pentagon documents and in speeches, it will provide intelligence analysts and law enforcement officials with instant access to information from Internet mail and calling records to credit card and banking transactions and travel documents, without a search warrant.

Historically, military and intelligence agencies have not been permitted to spy on Americans without extraordinary legal authorization. But Admiral Poindexter, the former national security adviser in the Reagan administration, has argued that the government needs broad new powers to process, store and mine billions of minute details of electronic life in the United States.

Admiral Poindexter, who has described the plan in public documents and speeches but declined to be interviewed, has said that the government needs to ''break down the stovepipes'' that separate commercial and government databases, allowing teams of intelligence agency analysts to hunt for hidden patterns of activity with powerful computers.