AP Photo

The headquarters of Pakistan's powerful Inter-Services Intelligence directorate is a black-ribbed stucco building in the Aabpara neighborhood of the capital. Its operatives, described by wary Pakistanis as "the boys from Aabpara," play a powerful and mysterious role in the life of the country. Their "tentacles," as one ISI officer terms the agency's spy networks, stretch deep into neighboring Afghanistan.

The ISI agreed to open its protective curtain slightly for me last week. This unusual outreach included a long and animated conversation with Lt. Gen. Ahmed Shuja Pasha, the agency's director general, as well as a detailed briefing from its counterterrorism experts. Under the ground rules, I cannot quote Pasha directly, but I can offer a sense of how his agency looks at key...