The Border Patrol nabbed two Pakistani men with ties to terrorism at the U.S.-Mexico border in September in the latest instance of illegal immigrants from so-called “special interest countries” using the southern border as a point of entry to the U.S. Muhammad Azeem and Mukhtar Ahmad, both in their 20s and from Gujrat, were caught Sept. 20 by agents south of San Diego and just over the international border from Tijuana. When agents checked their identities through databases they got hits on both of them: Mr. Ahmad popped up as an associate of a known or suspected terrorist, while Mr. Azeem’s information had been shared by a foreign government for intelligence purposes. Both men had been processed two months earlier by immigration officials in Panama, suggesting they took advantage of smuggling networks or other routes increasingly used by Central American illegal immigrants to sneak into the U.S. It comes as lawmakers on Capitol Hill are increasingly worried about potential terrorists gaining entry to the U.S. through its southern border or taking advantage of lax screening elsewhere in the immigration system. “The southern land border remains vulnerable to intrusion and exists as a point of extreme vulnerability,” Rep. Duncan Hunter, California Republican, wrote in a letter to Homeland Security Secretary Jeh Johnson last week demanding answers about how many people in the FBI’s terrorist screening database have been caught at the border. “Evidently there are criminal organizations and individuals with the networks and knowhow to facilitate illegal entry into the United States without regard for one’s intentions or status on a terrorist watchlist,” Mr. Hunter wrote. “The detention of the two Pakistani nationals underscores the fact that any serious effort to secure our homeland must include effective border security and immigration enforcement.” The FBI, whose agents were brought in to interview the two men, declined to talk about the case, saying it had “no information to provide.” The Border Patrol turned the men over to U.S. Immigration and Customs Enforcement (ICE), which said they have been in custody since September and are being held while they face immigration court proceedings. Other incidents have raised questions about the extent to which terrorists can take advantage of smuggling networks in Latin America. A year before the two Pakistani men were caught, the Border Patrol apprehended four Kurdish men who said they were part of the Revolutionary People’s Liberation Front/Party, which is listed by the U.S. as a terrorist organization. Mr. Johnson, the Homeland Security secretary, said the four were actually members of the Kurdish Workers Party, which is also listed as a terrorist organization by the U.S. government.