“I am not afraid of schisms. I pray that they do not happen,” Pope Francis said at a press conference on his plane returning to Rome from Madagascar on Tuesday, Sept. 10. He was responding to the question of whether he feared a schism in the United States church, given that some in that church, including a small number of both clergy and lay leaders, have been publicly and consistently critical of him in secular and Catholic media outlets.

Francis recalled that there have been schisms throughout the history of the church, including after the First Vatican Council and again after the Second Vatican Council, under John Paul II, with the Lefebvrites. He also characterized many groups in the contemporary church as having a “rigid” morality.

Today’s question followed an informal exchange between the pope and a French journalist on the flight from Rome to Maputo on Sept. 4. On that flight, Nicolas Senèze presented Francis with a copy of his new book, How America Wants to Change the Pope. The book describes how a wealthy and often traditionalist sector of the U.S. Catholic Church—both clerical and lay—has been highly critical of Pope Francis. In a private conversation with Mr. Senèze, the pope was overheard saying, “It was an honor to be attacked by the Americans,” referring to those mentioned in that book.

Pope Francis: “I don’t like it when the criticisms are made under the table, and they smile and show their teeth and then there is a knife in the back.”

Francis responded to six questions during the hour-long press conference, including three from journalists from the countries he had visited over this past week—Mozambique, Madagascar and Mauritius—and one from the Spanish news agency EFE about the environment and the Amazon region. The question about schism came at the end, and it prompted the pope to offer substantially new remarks.

It was asked by Jason Horowitz of The New York Times on behalf of the 15 or so English-language reporters on the flight. He inquired whether there was something about Francis’ pontificate that this sector of the U.S. church did not understand and whether he had learned anything from the criticisms. Then he asked whether Francis was afraid of a U.S. schism.

Pope Francis replied: “First of all, criticism is always useful, always. If someone receives criticism, he should immediately do a self-criticism and ask, ‘Is this true or not, or how much so?’ I always learn from criticism. Sometimes [criticisms] make you mad, but there are advantages.”

Referring to How America Wants to Change the Pope, he said, “I knew about the book, but I hadn’t read it.” In any case, he said, “the criticisms aren’t just from Americans, they are a little bit everywhere, even in the Curia. At least those who criticize [openly] have the honesty to say it. I like that. I don’t like it when the criticisms are made under the table, and they smile and show their teeth and then there is a knife in the back. This is not loyal; this is not human.”

“Today we have many, many schools of rigidity within the church that are not schisms but are pseudo-schismatic Christian ways.”

He added, “A critic that doesn’t want to hear the answer is [like] throwing a stone and then hiding your hand.” On the other hand, he said, “a loyal criticism” that has “openness to an answer is constructive. It is helpful.”

The pope offered the example of someone who says: “I don’t like the pope. [So] I criticize him and wait for the answer. I go to him, write an article and ask him to respond.” Francis said, “This is loyal, this is loving the church,” but “to criticize without wanting to hear the answer and without engaging in dialogue is not loving the church. It’s following a fixed idea: Change the pope, change the style, make a schism.”

Pope Francis recalled that “in the church there have been many schisms. After Vatican I…a sizable group left, and detached itself from the church,” referring to the Old Catholic Church that split off over the question of papal authority. “They had a different development, and today they ordain women, but in that moment they were very rigid. They followed an orthodoxy which thought that the council was wrong.”

The pope also said: “There is always schismatic action in the church. It is one of the actions that the Lord always leaves to human freedom…. I am not afraid of schisms. I pray that they do not happen, because the spiritual welfare of so many people is involved. [I pray] that there is dialogue, that there is correction if someone has gone wrong, but the journey in schism is not Christian.”

He recalled that the history of the church contains many heresies and schisms, saying that what they had in common was that the promoters of schisms “detach [themselves] from the people of God, from the faith of the people.” He said that “a schism is always an elitist state, from ideology detached from doctrine.”

Francis explained: “What I say on the social issues is the same that John Paul II said, the same. I copy him. But [some say], ‘This pope is too communist.’… Ideologies enter in the doctrine, and when doctrine slides into ideology there is the possibility of a schism.”

Referring to a “dry morality” imposed upon “the morality of the People of God,” the pope expressed concern about any ideology that is “so Pelagian” that it leads to rigidity. “Today we have many, many schools of rigidity within the church that are not schisms but are pseudo-schismatic Christian ways.”

Pope Francis concluded: “When you see Christians, bishops, priests [that are] rigid, behind this there are problems. There is not the holiness of the Gospel. For this we must be meek.” Of those who are rigid, he said, “They are going through a problem, and we must accompany them with meekness.”

Gerard O’Connell is America’s senior Vatican correspondent and author of The Election of Pope Francis: An Inside Story of the Conclave That Changed History. He has been covering the Vatican since 1985.