WASHINGTON—Only four large groups of migrants were caught trying to cross the U.S.-Mexico border since the Mexican government stepped up toughened enforcement in June, and no large groups have been seen so far this month, acting Homeland Security Secretary Kevin McAleenan told a House panel.

Mr. McAleenan said Thursday that while U.S. border authorities have encountered groups of more than 100 people in the past, with the biggest being more than 1,000 people, large-group crossings have declined in recent weeks.

“This...