Pope Francis, beginning a historic visit to Ireland, has said the Catholic church's failure to address clerical sexual abuse "remains a source of pain and shame", while the 26 County Taoiseach Leo Varadkar called for "zero tolerance" for those who abuse innocent children.

In the first of three planned speeches Pope Francis said he is "very conscious" of the circumstances of "our most vulnerable brothers and sisters." He was speaking to dignatories at Dublin Castle within hours of his arrival in Ireland and following a formal welcomed by President Michael D Higgins.

"The failure of ecclesiastical authorities - bishops, religious superiors, priests and others - adequately to address these repugnant crimes has rightly given rise to outrage and remains a source of pain and shame for the Catholic community," he said. "I myself share these sentiments."

Protests have been organised outside Dublin Castle and elsewhere along the Pope's two-day visit over the church's failure to act against paedophiles in their midst, as well as a series of scandals regarding the physical abuse of children and single mothers. In 2012, a mass grave of children was uncovered at a mother-and-baby home run by nuns in Tuam, County Galway.

Visiting Ireland to conclude the World Meeting of Families -- the first visit of a Pope to Ireland since 1979 -- Pope Francis also spoke warmly of the peace process and about the importance of recovering "the sense of being a true family of peoples".