In a speech to Catholic bishops from 22 Asian countries, the pope stressed the need to adopt a "creative" Catholicism that reflects the region's diversity and that listens with "empathy" to its different voices.
He made a particular appeal for better communications with nations like China, North Korea and Vietnam that do not have formal ties with the Vatican.
"I honestly hope that those countries of your continent with whom the Holy See does not enjoy a full relationship, may not hesitate to further a dialogue for the benefit of all," he told the bishops.
"Christians are not coming to Asia as conquerors," he said at a martyrs' shrine some 150 kilometres south of Seoul.
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It is the first papal visit for 15 years to Asia -- a region the Vatican sees as having enormous growth potential to offset dwindling numbers in the United States and Europe.
But nearly a dozen Asian countries in the region do not recognise the Vatican's authority over their Catholic communities, including China which remains the great elephant in the Vatican's Asian room.
Beijing and the Vatican have been at loggerheads since China severed ties with the Holy See in 1951.
In March last year, Beijing warned the newly elected Francis against interfering in China's internal affairs, "including under the pretext of religion".
The pope had offered his blessings in a message to China's President Xi Jinping as his plane flew over China on its way to South Korea last week.
An even more impenetrable country is North Korea, which carried out a series of short range-rocket launches into the sea just as the pope arrived in Seoul for his five-day visit.
Francis will focus on North Korea, which keeps all religious activity under the tightest control, when he holds a special Korean "peace and reconciliation" mass in Seoul before his departure tomorrow.