The reply was simple too, but not in a satisfying way. "We don't know," the official said.

The testy exchange during a recent congressional hearing between Representative Mark Meadows, Republican of North Carolina, and Alan Bersin, the assistant secretary for international affairs at the Department of Homeland Security, highlights what some law enforcement officials call a critical weakness in the United States foreign visa program.ntinue reading the main story

The issue has taken on added urgency as part of a broader examination of immigration policy following the mass shootings in San Bernardino, Calif., that left 14 people dead and 22 wounded. Tashfeen Malik, one of the attackers, was granted entry to the United States under a K-1 visa, also known as a fiancé visa. Her husband, Syed Rizwan Farook, was an American-born citizen. Both died in a shootout with the police. While Ms. Malik did not overstay her visa, the attack added to fears that a terrorist could exploit gaps in the system.

Nearly 20 years ago, Congress passed a law requiring the federal government to develop a system to track people who overstayed their visas. After the attacks of Sept. 11, 2001, an entry and exit tracking system was seen as a vital national security and counterterrorism tool, and the 9/11 Commission recommended that the Department of Homeland Security complete a system "as soon as possible." Two of the 9/11 hijackers, Satam al-Suqami and Nawaf al-Hazmi, had overstayed their visas.