A German bishop under pressure to resign for spending around €31 million on a luxurious residence said he had been heartened by a private audience with Pope Francis in Rome.

Bishop Franz-Peter Tebartz-van Elst of Limburg arrived in Rome more than a week ago after cost overruns on his residence stirred anger among German Catholics and protests outside his cathedral, at a time when the pontiff is stressing the importance of humility and serving the poor.

A statement released by Limburg diocese said the bishop was "grateful for the very heartening meeting". It added: "He and the Pope agreed the tenor and contents of their meeting would remain confidential."

The Vatican gave no details about the meeting, merely announcing it on the pope's daily list of audiences.

The media in Germany has dubbed Tebartz-van Elst "the luxury bishop" or "bishop bling" after an initial audit of his spending, ordered after a Vatican monitor visited Limburg last month, revealed the project cost at least six times more than planned.

Tebartz-van Elst has apologised for any "carelessness or misjudgement on my part" but denies wrongdoing.

The Pope has tried to set an example of austerity by renouncing the spacious papal apartments for a small residence in a Vatican guest house. He has also told bishops not to live "like princes".