WASHINGTON — The Trump administration is stepping up its pursuit of parents who paid to have their children illegally brought into the United States, according to people familiar with the matter. The effort, part of a widening crackdown on illegal immigration, is aimed at discouraging families from paying human smuggling organizations.

As part of a new round of immigration sweeps, officials are targeting parents or other relatives who were deported, re-entered the United States and then had their children smuggled across the border. Legal experts say cases of illegal re-entry are faster and easier to prove than a smuggling charge.

Immigration and Customs Enforcement officials said it was common for parents or family members in the United States to make illegal payments to smugglers to arrange for children to be brought to the border, where they turn themselves in and are often eventually handed over to their relatives. Tens of thousands of women and children have arrived at the border in the last three years, beginning with a surge of arrivals in the summer of 2014, many seeking refuge from gang violence and extreme poverty in Central America.

It was not clear how many people would be affected by the effort to arrest and prosecute family members for illegal re-entry, but officials familiar with the plan said it would serve as a deterrent to stop other parents and relatives from paying to have children brought to the United States as unaccompanied minors. The officials spoke on the condition of anonymity because they were not authorized to discuss enforcement policies publicly.