In the Elizabeth, N.J., neighborhood where Mr. Rahami lived and worked, such a program might — or might not — have made a difference. In recent years, for instance, some friends of Mr. Rahami’s noticed a significant change in his personality and religious devotion after a trip to Afghanistan, where he and his relatives are from. But there is no evidence that they alerted anyone, or expressed any concern.

Mrs. Clinton aims to set up an early-warning system, community by community. That builds on a growing number of programs that the Obama administration terms “countering violent extremism.” The aim is not just to rely on religious leaders such as imams to help detect the early signs of radicalization, but also to enlist teachers, coaches, physicians and others who might notice subtle changes in an individual’s behavior and, perhaps with family and friends, intervene.

Mrs. Clinton also suggested, in December, that she would accelerate work with technology companies to take radical speech off Facebook, YouTube, Snapchat and encrypted apps used by terrorists.

“You are going to hear all the familiar complaints: ‘Freedom of speech,’” she told the Brookings Institution. She suggested those complaints should be dismissed.

Her advisers acknowledge this would not constitute a complete solution — but neither would immigration bans, which they view as counter to American values.

“Look, we’re never going to be able to identify every potential bad actor solely through a police record or their involvement with other bad actors,” said Daniel Benjamin, a former State Department terrorism coordinator and now a scholar at Dartmouth College. “So having more eyes on this, and more awareness within communities, is absolutely essential, and will have to be a key part of the solution.”

Mr. Benjamin, who is an adviser to the Clinton campaign, acknowledged Tuesday that “there’s no guarantee that such programs would have identified Rahami ahead of time.” But he said Mr. Rahami’s case, and that of a Somali-American man who stabbed 10 people at a mall in St. Cloud, Minn., before he was shot and killed by an off-duty police officer, “appear to be examples of fairly dramatic changes in behavior that might have set off alarms.”