The meeting comes a day after Francis urged the world to take "decisive measures" to resolve the crisis that has forced more than 620,000 Rohingya Muslims to flee ethnic unrest in Myanmar for overstretched camps in Bangladesh.
Amid tight security, Francis, the first pope to visit Muslim-majority Bangladesh in 31 years, arrived in a locally- made popemobile -- a pickup truck covered in glass -- at Suhrawardy Udyan park where nearly 100,000 people waited to celebrate the mass.
Suborna Costa, 34, hoped the prayers of the 80-year-old pontiff will help end her family woes.
Costa's husband is ill, her brother went missing in Turkey after he illegally tried to enter Italy and one of her sisters has been unable to speak since childhood.
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"For years we don't have any good news in my family. My parents have been in shock since we lost contact with our brother," she said.
"I have been eagerly waiting for this day since his visit was announced several months ago. He is a saintly man and above any sin," said Costa.
"I feel like I am blessed to join the Pope's prayers. I'll pray for my late husband and parents so that they go to heaven. I hope the Pope will pray for peace and harmony among all communities in Bangladesh," she said.
The worries of the Rohingya masses who have packed camps on the Myanmar border have dominated the papal tour however.
Francis arrived in Dhaka on Thursday from Myanmar, where he walked a diplomatic tightrope, publicly avoiding allegations that the army is waging an ethnic cleansing campaign against the Rohingya.
Francis praised Bangladesh for giving refuge to the Rohingya who have flooded in since a military crackdown in Rakhine state in August.
"This has been done at no little sacrifice. It has also been done before the eyes of the whole world," he said, calling on other countries to offer "immediate material assistance to Bangladesh in its effort to respond effectively to urgent human needs".