In his first meeting with all the cardinals since his election as pontiff on May 8, Leo also asked the senior clerics to renew their commitment to major Church reforms enacted by the landmark Second Vatican Council in the 1960s.
Leo said Francis, who died on April 21, broadly had a vision of opening the staid 1.4 billion-member church to the modern world, had left an "example of complete dedication to service".
"Let us take up this precious legacy and continue on the journey," the new pope told the cardinals on Saturday.
The pontiff also asked the clerics to "renew together our complete commitment" to the reforms enacted by the council, which included celebrating the mass in local languages rather than Latin and pursuing dialogue with other religions.
He cited Francis's focus on "courageous and trusting dialogue with the contemporary world in its various components and realities".
Francis was pope for 12 years and often garnered criticism from conservative cardinals, who said he was watering down the church's doctrine on issues such as inclusion of LGBTQI Catholics and women's leadership.
Leo, the former US Cardinal Robert Prevost, was a relative unknown on the global stage before his election as pontiff.
He had spent most of his career as a missionary in Peru before serving as a senior Vatican official for the past two years.
The new Pope said on Saturday he had taken his papal name partly to honour Pope Leo XIII (1878-1903), who was known as an advocate for social justice and pushed for fair pay and treatment of workers during the industrial revolution.
Leo XIV said the church must take the lead in facing newer threats to workers, such as artificial intelligence.
He said AI posed "new challenges for the defence of human dignity, justice and labour".
Leo's two-hour meeting with the cardinals took a different format to that used by previous popes, who would typically offer a speech and expect the clerics only to listen.
This time, Leo gave a prepared address and then opened the floor to any cardinal who wanted to make a comment - allowing the clerics to voice their opinions and concerns about the main issues facing the global church.
"He listened very carefully, but he knows he's going to have to make the decisions," Irish Cardinal Sean Brady told Reuters. "But we're here to help him."
Spanish Cardinal Aquilino Bocos Merino described the meeting as "very cordial and communal."
Leo greeted each of the cardinals individually as they left the meeting, which was held in the same small Vatican auditorium where the cardinals had been gathering in the days before the conclave to discuss who should be the next pope.
