VATICAN CITY — Ban Ki-moon arrived at the Vatican with his own college of cardinals. Mr. Ban, the United Nations secretary general, had brought the leaders of all his major agencies to see Pope Francis, a show of organizational muscle and respect for a meeting between two global institutions that had sometimes shared a bumpy past but now had a mutual interest.

The agenda was poverty, and Francis inveighed against the “economy of exclusion” as he addressed Mr. Ban’s delegation at the Apostolic Palace. But in an informal meeting with Mr. Ban and his advisers, Francis shifted the discussion to the environment and how environmental degradation weighed heaviest on the poor.

“This is the pope of the poor,” said Robert Orr, who attended the May 2014 meeting as Mr. Ban’s special adviser on climate change and described the informal conversation with Francis. “The fact that he is making the link to the planet is really significant.”

On Thursday, Francis will release his first major teaching letter, known as an encyclical, on the theme of the environment and the poor. Given the pope’s widespread popularity, and his penchant for speaking out on major global issues, the encyclical is being treated as a milestone that could place the Roman Catholic Church at the forefront of a new coalition of religion and science.