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The 80-year-old pontiff's plane left Rome en route for Yangon, Myanmar's main city, shortly after 2100 GMT.
He will touch down around 0700 GMT on hoping to encourage efforts to contain a crisis that has seen many of the Rohingya, a Muslim ethnic minority in the mostly Buddhist Myanmar, forced from their homes and left languishing in squalid refugee camps over the border in Bangladesh.
"I ask you to be with me in prayer so that, for these peoples, my presence is a sign of affinity and hope," Francis told 30,000 believers in St Peter's Square, shortly before packing his bags for the diplomatically fraught trip.
Some 620,000 Rohingya, more than half their total number, have fled from Myanmar's Rakhine state to Bangladesh since August as a result of violence that the UN and the United States have described as ethnic cleansing.
Aides say Francis will seek to encourage reconciliation, dialogue and further efforts to alleviate the crisis following last week's tentative agreement between the two countries to work towards a return of some of the Rohingya to Myanmar.