The campaign encourages people to actually meet with migrants and listen to their stories, rather than treat them as statistics clouded by negative stereotypes.
Francis, the son of Italian immigrants to Argentina, launched the campaign during his weekly general audience, throwing his arms open to welcome the many refugees and asylum-seekers who filled St Peter's Square.
He urged individuals and governments to welcome migrants with similarly open arms and share in their plight, as Jesus did.
"Brothers, don't be afraid of sharing the journey. Don't be afraid of sharing hope," he said.
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The church is undertaking the campaign amid a hardening of anti-immigrant sentiment in the West.
In German elections this week, anti-migrant party Alternative for Germany secured seats in that country's parliament for the first time.
In the US, President Donald Trump is pressing for sweeping limits on immigration, including restricting travel from Muslim and other countries and slashing refugee admissions.
At the same time, he has acknowledged governments must manage refugee flows "with prudence," taking into account how many people it can successfully integrate into society.
"Christ urges us to welcome our brothers and sisters with our arms truly open, ready for a sincere embrace, a loving and enveloping embrace," he said.
Pointing to the colonnade that envelopes St Peter's Square, he said the embrace of migrants should mimic the colonnade, "which represents mother church who embraces everyone by sharing in our common journey."