The pope and the Church have come under increased attack because of their opposition to homosexual marriage and women priests. The pope has repeatedly denounced what he says are attempts to push religion out of public debate.
The 85-year-old pontiff celebrated Mass on the day Christians in the West mark the Epiphany, and ordained four new archbishops including his personal secretary.
In a homily to about 10,000 people in St Peter's Basilica in Vatican City, he firmly rejected suggestions the Church should change to suit public opinion.
"Anyone who lives and proclaims the faith of the Church is on many points out of step with the prevalent way of thinking," he said. "The approval of the prevailing wisdom, however, is not the criterion to which we submit."
In the United States, a group last month started a petition on the White House website asking the administration of President Barack Obama to list the Catholic Church as a "hate group" because of its opposition to gay marriage.
"Today's regnant agnosticism has its own dogmas and is extremely intolerant regarding anything that would question it and the criteria it employs," the pope said.