Pope Francis has told the Vatican's top administrators that his reforming agenda was like trying to clean Egypt's Sphinx with a toothbrush because of 'traitors' who stood in his way.

Francis has been repeatedly criticised by conservatives who have accused him of making pronouncements about major points of doctrine on the spur of the moment and confusing the faithful. He has faced particularly strong reactions to his encyclical Amoris Laetitia, which appeared to relax Church rules on communion for divorced and remarried people. He has refused to answer formal requests for clarification or retraction.

He used his annual Christmas lecture to the Curia, the Roman Catholic Church's central bureaucracy, to call for change.

Quoting a 19th-century Belgian clergyman, he said: 'Reforming Rome is like cleaning the Sphinx of Egypt with a toothbrush.'

According to Reuters, the humorous phrase did not evoke much laughter when the pope read it in the frescoed Clementina Hall of the Vatican's Apostolic Palace.

As well as his doctrinal forays, Francis has been attempting since his election in 2013 to bring the Church's hierarchy closer to its members, to enact financial reforms and guide it out of scandals that marked the pontificate of his predecessor, former Pope Benedict.

Some departments have been closed, merged or streamlined. But Francis said some in the bureaucracy were part of 'cliques and plots'. He called this 'unbalanced and degenerate' and a 'cancer that leads to a self-referential attitude'.

In his address on Thursday, he spoke of those 'traitors of trust' who had been entrusted with carrying out reforms but 'let themselves be corrupted by ambition and vainglory'.

When they are quietly let go, he said, 'they erroneously declare themselves to be martyrs of the system ... instead of reciting a "mea culpa"' (Latin for 'my fault').

He gave no specific examples.

Last June the Vatican's first auditor general resigned suddenly. He later said he was forced to step down because he had discovered irregularities but the Vatican said he had been spying on his superiors.

Earlier this month, the Vatican bank's deputy director was fired under circumstances that have not been explained.

In July, in a major shake-up of the Vatican administration, Francis replaced Catholicism's top theologian, a conservative German cardinal who has been at odds with the pontiff's vision of a more inclusive Church.

Francis said the overwhelming majority of Curia members were faithful, competent and some saintly.

Later, in a separate meeting with lay Vatican employees and their families, Francis asked forgiveness for the failings of some Church officials.

He spoke hours before the funeral of Cardinal Bernard Law, the ex-Archbishop of Boston who resigned in disgrace after covering up years of sexual abuse of children by priests and whose name became a byword for scandal in the Catholic Church.

Additional reporting by Reuters.