The Pope is in Malta on a pilgrimage in the footsteps of St Paul
Malta's president has referred to an abuse trial involving three Catholic clergy, in a speech marking the arrival of Pope Benedict on the island.
George Abela said justice had both to be done and seen to be done in the Maltese case. The priests are accused of sexually abusing orphaned children.
It is the Pope's first foreign trip since abuse scandals came to a head.
Pope Benedict made no direct reference to cases but did tell reporters the Church had been "wounded by its sins".
The pontiff is making a pilgrimage in the footsteps of St Paul.
The Pope's flight to Malta was one of the few to leave the Italian capital, Rome, amid the disruption caused by the Icelandic volcanic ash cloud.
The three Catholic priests are accused of sexually abusing 10 Maltese boys, who are now men, when they were in a Catholic orphanage in Malta.
Mr Abela told the Pope he believed it would be wrong "to try to use the reprehensible indiscretions of the few to cast a shadow on the Church as a whole".
"The Catholic Church remains committed to safeguarding children and all vulnerable people and to seeing that there is no hiding place for those who seek to do harm," he added.
It was the duty of both Church and state, he said, to establish "transparent mechanisms... together with harmonised and expeditious procedures in order to curb cases of abuse so that justice will not only be done but [be] seen to be done".
Mr Abela said that Malta, like the rest of the Western world, faced a conflict between Christianity and secularism.
"This profane character which has developed in some European states is driving people to be laicist or even anti-Christian," he said.
Praising a recent book by the Pope, Values in a time of Upheaval, he argued that "the moral foundations of a society as a whole, comprising believers, agnostics or atheists" were "better served not with the falling away from religion but with the reinvigoration of the moral consciousness of the state".
In brief remarks to journalists on board the flight from Rome, Pope Benedict XVI talked vaguely about sins that had wounded the Church.
"Malta loves Christ, who loves his Church, which is his body, even if this body is wounded by our sins," he said.
But his mention of a dark cloud that is over part of Europe referred not to the Church's crisis of credibility over sexual abuse scandals, but to the eruption of the Icelandic volcano, which at one moment threatened to scupper his pilgrimage, says the BBC's David Willey in Malta.
It is still unclear whether Pope Benedict will agree, during his short stay in Malta, to meet in private the alleged sex abuse victims, our correspondent adds.
The Pope's brief visit to the islands was originally planned as a pilgrimage commemorating the shipwreck of St Paul on the Mediterranean island in 60 AD.
The Pope has made no direct reference to the sex abuse scandals since writing a letter last month to the Catholics of Ireland expressing dismay at official reports of thousands of cases of Irish priests molesting children over a period of decades.
On Thursday, the Pope called on Roman Catholics to "do penance" for their sins, in an apparent reference to the crisis.