A statement said British Bishop Richard Williamson must "unequivocally" distance himself from his statements to serve in the Roman Catholic Church.
The Vatican also said that the Pope had not been aware of the bishop's views when he lifted excommunications on him and three other bishops last month.
Earlier, a senior cardinal acknowledged the Vatican had mishandled the issue.
The Pope's decision, ending Bishop Williamson's excommunication on an unrelated matter, has caused a bitter row, as the bishop does not believe that Jews were gassed by the Nazis in World War II.
The BBC's David Willey in Rome says it is almost unheard of for a pope to admit publicly that he has made a mistake. But that is in effect the significance of the urgent statement put out by the Vatican, our correspondent adds.
"Bishop Williamson, in order to be admitted to the Episcopal functions of the Church, must in an absolutely unequivocal and public way distance himself from his positions regarding the Shoah [Holocaust]," it said.
It said Bishop Williamson's positions on the Holocaust were "absolutely unacceptable and firmly rejected by the Holy Father".