The Pope also "expressed his shame and sorrow over what victims and their families have suffered", a Vatican statement said.
The meeting, in private, took place at the end of the Pope's visit to Malta.
Three priests are accused of sexually abusing orphan children on Malta in the 1980s and 1990s.
In Malta, 10 men have testified that they were sexually molested by Catholic priests at an orphanage during that time. They had asked to meet Pope Benedict to close what they have termed a "hurtful chapter" in their lives.
'Spiritual courage'
"The Holy Father met a small group of persons who were sexually abused by members of the clergy," the statement said.
"He prayed with them and assured them that the Church is doing, and will continue to do, all in its power to investigate allegations, to bring to justice those responsible for abuse and to implement effective measures designed to safeguard young people in the future.
"In the spirit of his recent Letter to the Catholics of Ireland, he prayed that all the victims of abuse would experience healing and reconciliation, enabling them to move forward with renewed hope," the statement added.
It provided no further details of what measures would be implemented.
One of the alleged abuse victims in Malta later said the meeting with the Pope - which lasted about 45 minutes - had given him huge spiritual courage.
Speaking on local television, Lawrence Grech sobbed and was very emotional.
He said he was now a lapsed Catholic, after his childhood experiences. But he added that he thought the Pope should not carry on his shoulders the guilt of others in the paedophile priest scandals.
Reservations
This was the first time the pontiff had met with alleged victims since the worldwide clerical abuse row erupted this year.
Ahead of the Pope's visit, the official Vatican spokesman, Father Federico Lombardi, said that the pontiff would not agree to any meeting in the full glare of media publicity, and that the crowded programme during the 26-hour visit to Malta was unlikely to leave a window for such an opportunity.
On Saturday, the Archbishop of Malta, Paul Cremona, told worshippers at a Mass attended by the Pope that the Catholic Church must recognise what he called the failures and sins of its members.
The Pope had hitherto maintained silence on the abuse crisis, which has overshadowed his visit, the BBC's David Willey in Malta reports.
On Saturday, the pontiff was greeted outside the presidential residence by several thousand Maltese children singing happy birthday to the pontiff, who had just turned 83.
The Pope is making a pilgrimage to the Mediterranean island in the footsteps of St Paul.
Before leaving for Rome, Benedict is due to address thousands of young Maltese Catholics who have been invited to meet him on the quayside in Valletta.
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