Cardinal Gerhard Müller, the Vatican's doctrinal chief, says individual bishops cannot reinterpret Church teaching subjectively.
However, he added, "I do not think it is particularly beneficial for each individual bishop to comment on papal documents to explain how he subjectively understands the document."
In recent weeks, the bishops of Malta and Germany have issued guidelines permitting Communion for the remarried.
The Maltese bishops said that it might be "impossible" for some couples to avoid sex, and that people could not be refused Communion if they discerned that they were "at peace with God".
However, several bishops have affirmed the traditional teaching that the remarried cannot receive Communion, except when they endeavour to live "in complete continence".
"It cannot be that the universally binding doctrine of the Church, formulated by the Pope, is given different and even contradictory regional interpretations. The basis of the Church is the unity of faith. The Church no longer experiences a new revelation," he said.
Cardinal Müller also said that, in order to be absolved of adultery, a penitent must resolve not to sin again. He said: "No one can alter the sacraments as a means of grace according to their own choice – for example, so that the sacrament of Confession can be given without the intention to sin no more."
Elsewhere in the interview, the Cardinal said he thought papal resignations would remain a rare exception in future. He also said that it was important to honour Church leaders because of their role, not just because of their human qualities.
"Everyone is weak and mortal," he said. "Jesus did not choose the wisest, the richest, and the most prominent among his apostles, but simple people, craftsmen, fishermen. We depend on the grace of God and not on what we achieve every day.