Pope Francis has apologised for his widely-viewed slap of a woman who grabbed his hand as he greeted Catholic faithful on New Year's Eve.

The image of Francis slapping his way free from the clutches of the admirer was viewed widely on social media.

A personal apology followed.

"We lose patience many times," Francis confessed.

"It happens to me too. I apologise for the bad example given yesterday," the head of the Catholic church said before celebrating mass at the Vatican.

Francis had greeted children before the Nativity scene on Saint Peter's square and was turning away when the woman who had crossed herself then cried out something, pulled on his hand and almost caused him to fall.

The 83-year-old pope grimaced before managing to break free by slapping her hand.

He continued his tour, walking with some difficulty while maintaining a slightly greater distance from visitors, and gradually relaxed again as he came into contact with other children.

Twitter comments were mostly supportive of the pontiff's instinctive reaction.

The Pope also said women were "the source of life" but deplored that they were constantly "offended, beaten, abused and forced into prostitution" and forced to "suppress the life they carry within" them.

He emphasised that the "rebirth of humanity began with a woman", and bemoaned that women's bodies were "sacrificed on the profane altars of advertising, profit, pornography".