Pope Benedict XVI was baptizing seven adults during the service, which marks the period between Good Friday, which commemorates Jesus' crucifixion, and Easter Sunday, which marks his resurrection.
The Vatican spokesman, the Rev. Federico Lombardi, said of Allam before the service that anyone who chooses to become a Catholic of his or her own free will has the right to receive the sacrament.
Lombardi said the pope administers the sacrament "without making any 'difference of people,' that is, considering all equally important before the love of God and welcoming all in the community of the Church."
Benedict opened the lengthy nighttime service by blessing a white candle, which he then carried down the main aisle of the darkened St. Peter's Basilica. Slowly, the pews began to light up as his flame was shared with candles carried by the faithful, until the whole basilica twinkled and the main lights came on.
The baptism rite during the vigil service is part of the joyful renewal Christians associate with Easter.
There is no overarching Muslim law on conversion. But under a widespread interpretation of Islamic legal doctrine, converting from Islam is apostasy and punishable by death - though killings are rare.
Egypt's highest Islamic cleric, the Grand Mufti Ali Gomaa, wrote last year against the killing of apostates, saying there is no worldly retribution for Muslims who abandon their religion and that punishment would come in the afterlife.
Osama bin Laden accused the pope in a new audio message posted Wednesday of playing a "large and lengthy role" in a "new Crusade" against Islam that included the publication of drawings of the Prophet Muhammad that many Muslims found insulting.
Lombardi said Thursday that bin Laden's accusation was baseless. He said Benedict repeatedly criticized the Muhammad cartoons, first published in some European newspapers in 2006 and republished by Danish papers in February.