WASHINGTON — Hundreds of immigrant families caught illegally crossing the Mexican border told U.S. immigration agents they made the dangerous journey in part because they believed they would be permitted to stay in the United States and collect public benefits, according to internal intelligence files from the Homeland Security Department.

The interviews with immigrants by federal agents were intended to help the Obama administration understand what might be driving a puzzling surge in the numbers of border crossings that started over the summer. The explanations suggest the U.S. government’s efforts to discourage illegal crossings may have been unsuccessful. Its efforts have included public service campaigns in Honduras, El Salvador and Guatemala to highlight the dangers and consequences of making the trek across Mexico to cross illegally into the United States.

The Associated Press obtained copies of the interview summaries, which were compiled in reports by the U.S. Customs and Border Protection’s Office of Intelligence. They said hundreds of people traveling as part of families consistently cited opportunities to obtain permission to stay in the U.S., claim asylum and receive unspecified benefits. Immigrants spoke of “permisos,” or a pass to come into the United States.

The report “is not intended to be a comprehensive analysis of the situation,” said department spokeswoman Marsha Catron, adding that troubles in the immigrants’ home countries likely contributed to their flight as well.

Although the Obama administration has explained that immigrants who cross the U.S. border illegally can be deported, lengthy backlogs of more than 456,000 cases mean that immigrants can effectively remain in the U.S. for years before a judge decides whether they should leave the country. Also, recent court rulings have complicated the government’s plans to hold families in immigration jails pending deportation proceedings. Immigrants living in the U.S. illegally generally are not eligible for public benefits, except that children may receive free or reduced meals in public schools.