"Let's not close our hearts, let's not look to the other side", the pope said during an interfaith prayer for peace in Dhaka, according to Crux, a Catholic news website.
He told them "I ask your forgiveness for the indifference of the world" to their plight in fleeing brutality and rape in Myanmar. After the meeting with the pope, some of the Rohingyas cried, witnesses said. "I appeal to your large hearts to give us the forgiveness that we are asking", Francis added.
Through translators, he also spoke to a group of Rohingya refugees from three families, Crux reported, including 12 men, two women in niqabs, and two girls.
Pope Francis' speeches during his trip to Myanmar and Bangladesh have been watched closely, to see if he would use the word "Rohingya" to describe these refugees.
Earlier, the Pope ordained 16 priests at an outdoor Mass in Dhaka's Suhrawardy Udyan park.
Many in Myanmar reject the term "Rohingya" and instead refer to the group as illegal immigrants from Bangladesh.More news: Playoff top 4 might not stay as is
Soon after arriving from neighbouring Myanmar late on Thursday he urged the world to take "decisive measures" to resolve the crisis that has forced more than 620,000 Rohingya Muslims fleeing ethnic unrest across the border into overstretched camps in Bangladesh.
Security was tight for Friday's mass, which follows a rise in attacks on religious minorities in Bangladesh by Islamist extremists.
Vatican spokesman Greg Burke dismissed the idea that the Pope diminished his moral authority by avoiding a direct reference to the group during his visit to Myanmar, the first by a Pope to the Buddhist-majority country.
But speaking to Muslim, Buddhist and Hindu leaders, Francis praised the country's commitment to religious freedom, which he said "stands as a subtle yet firm rebuke to those who would seek to foment division, hatred and violence in the name of religion". "I hope the Pope will pray for peace and harmony among all communities in Bangladesh".
Pope Francis is known for championing the rights of refugees and has repeatedly expressed his support for the Rohingya, a persecuted Muslim minority whom he has described as his "brothers and sisters". He became the first Catholic leader to visit Dhaka since 1986.
Christians make up less than 0.5 percent of officially secular Bangladesh's population of 160 million and community leaders say it has become more hard to practise their faith openly.