Speaking after a trip to Africa, the Pope took issue with conservative clergymen who have criticised him.
Those men do not "want good for the Church", but only care about "changing popes, changing styles, creating a schism", he said.
US Catholic leaders have attacked the Pope in the past for his views.
It is the first time he has spoken so openly about the chance of a split in the Church, which has more than one billion followers worldwide.
What did the Pope say?
Pope Francis made his comments on a flight back to Rome after a trip to Madagascar, Mauritius and Mozambique.
He was asked by a reporter about attacks from conservative Catholic leaders, TV channels and websites in the US.
Some Catholic leaders - particularly in the US but also some others around the world - have accused the Pope of diluting their faith, and have even called for his resignation.
They are unhappy with his stances on the environment and immigration. But in particular they are opposed to his moves to allow divorced and remarried Catholics to take Communion.
"I'm not afraid of schism," Pope Francis said, adding that many had happened in the history of the Church. "I pray that there won't be one, because the spiritual health of many people depends on it."
Pope Francis suggested political ideology was tainting his critics' views of him.
"The things I say about social issues are the same things [Pope] John Paul said. I copy him [and they say] 'the pope is too communist'," he told reporters.
He praised "constructive criticism", but not "those who smile while stabbing you in the back".
"The criticisms do not only come from the Americans [but] from everywhere, including the Curia," he said, referring to the Catholic Church's governing body.
Has the church split before?
In its 2,000-year history the Catholic Church has split a number of times, most notably in 1054, when the Eastern Orthodox Church split off from Rome.
Other splits have led to the rise of antipopes - other men who claim to be the pope and refuse to bow to Rome. Antipope Benedict XIII granted the University of St Andrews in Scotland its university status in 1413.
More recently, French Archbishop Marcel Lefebvre ordained four bishops without papal approval in 1988.--BBC