Gunmen raided the building on Friday, handcuffing victims and shooting each in the head.
The attack at the facility run by Catholic missionaries in the port city of Aden left four nuns dead, the Vatican reported.
"These are the martyrs of today," Francis said Sunday in St. Peter's Square, calling the nuns not just victims of the attackers but also of "indifference, of this globalization of indifference, that does not care."
The nuns were part of a group founded by soon-to-be-sainted Mother Teresa
. Two were from Rwanda, one was from India and the fourth one was from Kenya.
In his prayer, Francis called on Mother Teresa to "accompany in heaven these daughters, martyrs for charity, and intercede for peace and sacred respect for human life."
Al Qaeda militant group: 'It's not our way of fight'
Ansar al-Sharia, an umbrella group for al Qaeda militants in Yemen, said it is not responsible for the attacks. It warned journalists to avoid reporting that it is responsible.
"Our honorable people of Aden, we Ansar al-Sharia deny any connection or relation to the operation that targeted the elders' house," the group said in a statement Sunday. "This is not our operation and it's not our way of fight."
It was not immediately clear who carried out the attack.
The unusual statement stands in a sharp contrast with previous responses from al Qaeda and other terror groups, which have proudly claimed responsibility for other attacks.
Vatican condemns attackers
On Saturday the Vatican sharply rebuked the gunmen and urged a resolution.
The Pope "prays that this pointless slaughter will awaken consciences, lead to a change of heart and inspire all parties to lay down their arms and take up the path of dialogue," Vatican Secretary of State Pietro Parolin said.
Months of violence
The impoverished Muslim nation has faced violence for years, some of it tied to al Qaeda elements that call it home.
The latest round of unrest started in 2014 amid angry protests by Houthis, a minority Shiite group that's long held sway in northern Yemen, but hasn't had much influence in the Sunni-led government.
The Houthi rebels seized the presidential palace in January last year, forcing out President Abdu Rabu Mansour Hadi on the way to taking over Sanaa, the capital city, and other areas.
Those strikes have continued months later, as has the bloodshed.
The fighting is taking a "terrible toll" on Yemenis, said spokesman Rupert Colville for the U.N. high commissioner for human rights
In January, he reported over 8,100 casualties, including 2,800 deaths. That number is expected to go up when new numbers are released.