Border officials from October to May have documented 4,800 members of families in which an adult who claimed to be related to a child in his or her possession was not the parent, just under 1.5% of the 332,981 total illegally entering family members, according to the Department of Homeland Security.

"We have identified now more than 4,800 family units that were fraudulent as they presented at the border," acting DHS Secretary Kevin McAleenan told the Senate Judiciary Committee Tuesday. The family units tally represents the number of individuals, either a child under 18 years old, parent, or legal guardian, apprehended with a family member by the U.S. Border Patrol, according to the DHS.

The new DHS chief said some migrants seeking to gain entry into the U.S. are paying smugglers to rent a child because families from countries other than Mexico and Canada cannot be held in federal custody more than 20 days.

However, the percentage of migrants using unrelated children to avoid immediate deportation is very low compared to the number of related families.

McAleenan also said the department has "uncovered multiple child smuggling rings" but did not share additional information.

Immigration and Customs Enforcement, the DHS agency that takes custody of people after Border Patrol have initially processed them, said it found more than 400 "fraudulent" family members over the most recent six week span measured, from mid-April to May 31. That figure is included in the overall DHS 4,800 figure.