The pontiff and President Paul Kagame, met at the Vatican on Monday.
At the meeting, the Pope acknowledged that some Catholic priests and nuns "succumbed to hatred and violence, betraying their own evangelical mission."
The Vatican said the Pope also "expressed the desire that this humble recognition of the failings of that period, which unfortunately disfigured the face of the church, may contribute to a 'purification of memory' and may promote, in hope and renewed trust, a future of peace".
An estimated 800,000 Rwandans - mostly Tutsis - were killed in the space of 100 days between April and June 1994 by Hutu extremists.
Many of the country's victims died at the hands of priests and nuns according to accounts by survivors. It is believed that some clergy allowed government soldiers and organised gangs to demolish or blow up churches where Tutsis and moderate Hutus had taken refuge.
Last year, the Catholic Church in Rwanda issued an apology for their involvement in the massacre.