Representatives Hakeem Jeffries, a Democrat from Brooklyn, and Doug Collins, a Republican from Georgia, sponsored the bill, which Mr. Jeffries said would correct an emerging inequity in the criminal justice system.

“I assume that most fair-minded prosecutors understand that our system of justice requires a dynamic where individuals are able to have the effective assistance of counsel necessary to adequately defend themselves,” Mr. Jeffries said in an interview, adding that “email is the most efficient way for an attorney to communicate with an incarcerated client.”

The New York Times reported last year that federal prosecutors in Brooklyn had alerted defendants that their emails would be monitored, a practice that was occurring in spots around the country.

Brooklyn federal prosecutors argued that prisoners had to agree to terms of service telling them that emails could be monitored when they used the Bureau of Prisons’ email system. Prosecutors said it was a logistical issue: The bureau’s system could not distinguish emails to lawyers from other messages, which are automatically monitored. The office of the United States attorney for the Eastern District of New York no longer wanted to appoint “taint teams” to sort through the emails, as it had been doing.
Defense lawyers in a handful of cases in Brooklyn had objected to that, arguing that it hindered the right to counsel. In-person visits, postal mail and phone calls are all considered protected by lawyer-client privilege. However, arranging such interactions was inefficient, lawyers said — a single visit to a jail could take several hours of travel and waiting. They needed access to unmonitored email, they argued, to provide effective counsel.

Federal judges in Brooklyn, and around the country, were split on the issue. In one case last year, a district judge, Dora L. Irizarry, instructed prosecutors to stop the practice, suggesting they were looking for a strategic advantage. “You’re going to tell me you don’t want to know what your adversary’s strategy is? That’s hogwash,” Judge Irizarry told a prosecutor.

In another case, another district judge, Allyne R. Ross, ruled that because defense lawyers had other ways of communicating confidentially with their clients, the government’s policy did not unreasonably impinge on the defendant’s rights, and she allowed the practice to continue.

Mr. Jeffries said that he had spoken to the Bureau of Prisons, and that people at the agency said its email system did not allow inmates’ emails to lawyers to be filtered from other emails.

“We live in an era where there’s been tremendous innovation that has taken place across every spectrum of our economy,” he said. “It seems to me that we have the ability to develop a system where attorney-client communication can be segregated out.”

The Bureau of Prisons referred a request for comment to the Justice Department, which did not immediately respond.

Alan Dayley, a research director at Gartner, a technology-information company, said a number of tools were available to capture emails based on criteria such as “sent to” or “received from,” and the tools “can also capture certain email based on content.”

The bill would allow an exception in cases where the attorney general believes there is a national security issue.

Doug Jones, a former United States attorney for the Northern District of Alabama who is now in private practice, said the legislation was sensible.

“It’s a very difficult representation to represent a client who is in custody,” Mr. Jones said.

He gave the example of Birmingham defendants who were kept at a county jail three blocks from him. “You wouldn’t think that would be a problem, but it’s an itty-bitty room; it’s hard to bring tapes and transcripts and other things,” he said, adding that it was also difficult to contact a client with a quick question.

Donald K. Stern, a former United States attorney for Massachusetts, said that while there would no doubt be some cost to overhauling the email system, there was also a cost to the current setup. Court-appointed defense lawyers who have to spend several hours trying to visit their clients are ultimately paid by the government, he pointed out.

“You have to balance the cost of doing that with the importance of permitting the ability of counsel to communicate freely with a client,” Mr. Stern said. “The lawyer ought to be able to have very free access to their clients — not only for the right to counsel and the Sixth Amendment, but also to provide a more efficient and fair criminal justice system.”