The pontiff has been making a pilgrimage in the footsteps of St Paul
Pope Benedict is to end his first foreign trip since the child sex abuse scandals came to a head with an open-air Mass in Malta's capital, Valletta.
The Pope only referred to the priest sex abuse scandal in the most general terms on Saturday.
Three priests are being accused of sexually abusing orphan children on Malta in the 1980s and 1990s.
Maltese President George Abela has called for justice to be done and to be seen to be done.
The BBC's David Willey says Pope Benedict is unlikely to agree to a meeting requested by the 10 Maltese men who allege in criminal proceedings that, as children, they were sexually molested by the priests at the orphanage.
The Pope was greeted outside the presidential residence on Saturday by several thousand Maltese children singing happy birthday - he had just turned 83 - and will address thousands more young people at a quayside meeting just before he returns to Rome.
But he appears unwilling to refer to the subject of paedophile priests or even to mention the words in public, our correspondent says.
The pontiff is making a pilgrimage to the island in the footsteps of St Paul.
His flight to Malta was one of the few to leave the Italian capital, Rome, amid the disruption caused by the Icelandic volcanic ash cloud.
Greeting the Pope on Saturday, Mr Abela said 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.
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.