The 80-year-old pope, the first to travel to Myanmar, received Senior General Min Aung Hlaing at the archbishop's residence in Yangon, where the pontiff will stay during his visit.
The UN and US accuse the army which the general controls of "ethnic cleansing" in a campaign that has driven more than 620,000 Rohingya from Myanmar's northern Rakhine state into neighbouring Bangladesh since August.
During a 15-minute meeting the pontiff and the army chief spoke of the "great responsibility of the country's authorities in this moment of transition", the Vatican spokesman Greg Burke said.
Myanmar was ruled by a junta for five decades until a civilian government led by Aung San Suu Kyi came to power last year.
Earlier today Francis was welcomed at Yangon's airport by children from different minority groups in bright bejewelled clothes, who gave him flowers and received a papal embrace in return.
"I saw the pope... I was so pleased, I cried!" Christina Aye Aye Sein, 48, told AFP after the pope's convoy received a warm but modest welcome.
"His face looked very lovely and sweet... He is coming here for peace."
Myanmar's estimated 700,000 Catholics make up just over one percent of the country's 51 million people.
But around 200,000 Catholics are pouring into Myanmar's commercial capital Yangon before a huge open-air mass on Wednesday.
"People came from all corners of the country, even if we could only see him for a few seconds," Sister Genevieve Mu, an ethnic Karen nun, told AFP.
Tmorrow Francis will meet Suu Kyi, a Nobel Peace Prize winner whose lustre has faded because of her failure to speak up publicly for the Rohingya.
He will hold two masses in Yangon.
Speaking shortly before he left Rome, the pontiff said: "I ask you to be with me in prayer so that, for these peoples, my presence is a sign of affinity and hope."
But rights groups, the UN and the US have accused the military of using its operation as cover to drive out a minority it has oppressed for decades.
The deluge of desperate refugees arriving in Bangladesh have carried with them accounts of murder, rape and arson at the hands of troops and Buddhist mobs.
Inside the country opinion differs sharply from the rest of the world.
Days before the papal visit, Myanmar and Bangladesh inked a deal vowing to begin repatriating Rohingya refugees in two months.
But details of the agreement - including the use of temporary shelters for returnees, many of whose homes have been burned to the ground - raise questions for Rohingya fearful of returning without guarantees of basic rights.
Francis will travel on to Bangladesh on Thursday, where he will meet a group of Rohingya Muslims in the capital Dhaka.
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