VATICAN CITY — On Thursday night, Bernie Sanders was standing under the lights in Brooklyn, being pressed by journalists and his rival at the Democratic debate, Hillary Clinton, to provide details about his often-vague policy ideas.

Less than 12 hours later, and more than 4,000 miles away, near the residence of Pope Francis, Mr. Sanders was basking in the attention of appreciative figures from around the world and fielding questions he seemed to enjoy.

“My perception is that the access to quality education is very unequal in the United States,” Juan José Llach, a former education minister in Argentina, said in addressing the senator. “I don’t know if I’m wrong.”

Mr. Sanders wasted no time parlaying his answer about struggling urban schools and student debt into an argument for one of his signature campaign policies: tuition-free public colleges.