The Pope's statement, which he said he hoped would help Rwanda heal, followed a meeting in Rome with Rwandan President Paul Kagame.
In November, Rwanda's Catholic Church apologized for its members' role in the genocide.
"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 promote renewed trust", the Vatican added. An estimated 800,000 Tutsis and moderate Hutus were killed in a genocide that lasted 14 days while the world watched on. Others testified that the clergy betrayed people who tried to seek refugee in Catholic churches.
The genocide in Rwanda - which the United Nations acknowledged to have been planned by the then government - was sparked by the assassination of former President Juvenal Habyarimana, which saw the majority Hutu ethnic group descend upon the minority Tutsi. The Church was compromised by its long-standing political ties to the ruling Hutu elite.
Some priests have been accused of handing over people with no way out to the militia.
The ministry of local government rejected the apology then as inadequate.
Both Pope Francis and President Paul Kagame acknowledged that while many priests and nuns took part in the killings in Rwanda, there were some who were victims themselves.
Sterling flips lower after United Kingdom sets Brexit talks trigger date
The Prime Minister will trigger Article 50 on March 29 and has insisted that Parliament will get a vote on the final Brexit deal. She will contact Tusk directly to launch negotiations in due course.
Ibuka, the umbrella body of organisations representing Genocide survivors, has thanked President Paul Kagame for initiating the dialogue with the Vatican.
Ever since the case against the murderous priests has been established in the aftermath of the genocide, the Roman Catholic Church has not only smuggled those priests out of Rwanda, they have made sure that the arms of law never caught up with them. While some priests in Rwanda refused to read the apology to their members, the latest comment by the Pope shows the church has come of age to fully accept what it did.
Athanase Seromba, for instance, a Rwandan Catholic priest, was convicted in 2006 of aiding and abetting genocide and subsequently sentenced to 15 years in prison.
"It allows us to build a stronger base for restoring harmony between Rwandans and the Catholic Church", Rwanda's Foreign Minister Louise Mushikiwabo said in a separate statement.
"I don't understand why the pope would apologize for sexual offenses, whether it is in the US, Ireland or Australia, but can not apologize for the role of the church in the genocide that happened here", Mr. Kagame said a year ago.
Mushikiwabo said the church's teachings laid the foundation for genocide ideology, "Today, genocide denial and trivialization continue to flourish in certain groups within the church and genocide suspects have been shielded from justice within Catholic institutions".