WASHINGTON — As the nation’s spy agencies assess the fallout from disclosures about their surveillance programs, some government analysts and senior officials have made a startling finding: the impact of a leaked terrorist plot by Al Qaeda in August has caused more immediate damage to American counterterrorism efforts than the thousands of classified documents disclosed by Edward Snowden, the former National Security Agency contractor.

Since news reports in early August revealed that the United States intercepted messages between Ayman al-Zawahri, who succeeded Osama bin Laden as the head of Al Qaeda, and Nasser al-Wuhayshi, the head of the Yemen-based Al Qaeda in the Arabian Peninsula, discussing an imminent terrorist attack, analysts have detected a sharp drop in the terrorists’ use of a major communications channel that the authorities were monitoring. Since August, senior American officials have been scrambling to find new ways to surveil the electronic messages and conversations of Al Qaeda’s leaders and operatives.

“The switches weren’t turned off, but there has been a real decrease in quality” of communications, said one United States official, who like others quoted spoke on the condition of anonymity to discuss intelligence programs.

The drop in message traffic after the communication intercepts contrasts with what analysts describe as a far more muted impact on counterterrorism efforts from the disclosures by Mr. Snowden of the broad capabilities of N.S.A. surveillance programs. Instead of terrorists moving away from electronic communications after those disclosures, analysts have detected terrorists mainly talking about the information that Mr. Snowden has disclosed.