Pope Francis has apologised for hitting the hand of a well-wisher who grabbed him and yanked him towards her.

In his new year wishes to the public in St Peter's Square, Francis confessed to losing his patience with the woman while he was walking in the square on Tuesday night to admire the Vatican's Nativity scene.

Cameras captured the scene when the woman, from behind a barrier, reached out and grabbed the pope's hand, pulling him violently towards her.

Francis reacted sharply, exclaimed something and then slapped her hand so she would let him go.

Frowning in anger, he turned and strode away.

In his impromptu remarks on Wednesday, Francis said "so many times we lose patience. Me too".

He then added "I say 'excuse me' for the bad example" he gave in the incident on Tuesday.