He said he realised his words hurt many, but repeated his belief that Chilean Bishop Juan Barros was innocent.
The pontiff was speaking to journalists on board a plane flying back to Rome.
Last week, he had said that victims who had accused Bishop Barros were committing slander.
The Pope was openly criticised by Cardinal Sean O'Malley of Boston, who said he left victims of sexual abuse committed by priests feeling abandoned.
"I apologise to them if I hurt them without realising it, but it was a wound that I inflicted without meaning to," said the Pope on Monday, as quoted by Reuters news agency. "It pains me very much."
Bishop Barros has not been accused of abuse, but of being present when another priest, Fernando Karadima, molested young boys.
When questioned by a Chilean journalist on Thursday, the Argentine pontiff had said: "The day they bring me proof against Bishop Barros, then I will speak. There is not a single piece of proof against him. Everything is slander. Is this clear?"
This prompted some of Karadima's victims to hold a press conference where they said it was "offensive and unacceptable to say that we need to provide concrete evidence".
On Monday, the Pope said he regretted using the word "proof", saying he realised that it came off as a slap in the face.
"There are lots of abused people who cannot show proof. They don't have it. Or they have it but they keep it to themselves, suffering in silence," he said.