During talks with a Catholic delegation from Nigeria, the pope demanded that priests and church members in the southern diocese of Ahiara write to him personally to "ask his forgiveness", the Holy See said in a statement at the weekend.
"In the letter, one must clearly manifest total obedience to the pope, and whoever writes must be willing to accept the bishop whom the pope sends and has appointed," said the statement.
"Whoever does not do this will be ipso facto suspended a divinis and will lose his current office," it warned.
The dispute involves Monseigneur Peter Okpaleke who was named bishop of the Ahiara diocese in 2012 by Pope Benedict, Francis' predecessor.
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But his appointment was rejected on ethnic grounds by the local priests, who protested over the fact the Vatican had not named someone from their own diocese.
As a result, Cardinal John Onaiyekan, the archbishop of Abuja, was appointed the following year as the apostolic administrator of the diocese.