In an interview with the Munich-based Focus magazine, Archbishop Gerhard Müller said the two sides were drifting further and further apart.
The time had come for the CDF to insist that the in-fighting stop because it was harming the Church, he said. Factionalism was a symptom of disease, he pointed out.
Catholics must ask themselves whether their loyalty to a particular group is greater than their desire for unity, he said.
The conservative Society of St Pius X (SSPX) was a "loose association of priests who cannot claim to represent the Catholic Church", he added.