The pontiff delivered the message during his annual holiday comments at the Hall of Blessings in St. Peter's Basilica.
"At Christmas, we celebrate the light of Christ that comes into the world, and he comes for all, not just for some," Pope Francis said.
"Today, at this time of darkness and uncertainty because of the pandemic, there appear different lights of hope, such as the discovery of vaccines."
Pope Francis urged world leaders, pharmaceutical companies and international agencies "to promote cooperation and not competition" in guaranteeing widespread availability of COVID-19 vaccines from multiple companies like Pfizer, Moderna and Astrazeneca.
"But so these lights may illuminate and bring light to the whole world, [the vaccines] must be available to all. I cannot put myself before others, placing the laws of the market and of patents above the law of love and the health of humanity."
Francis also offered prayers for other victims around the world, and asked for peace in countries like Syria, Iraq and Yemen that are still scarred by war. He also expressed hope for the end of suffering in Lebanon, which has had a tumultuous year, and continued dialogue in the perpetual drive for Israeli-Palestinian peace.
"In everyone, I see reflected the face of God, and in those who suffer, I see the Lord pleading for my help," he said. "I see him in the sick, the poor, the unemployed, the marginalized, the migrant and the refugee."
At his annual Christmas Eve Mass late Thursday, the pope echoed similar sentiments for the needy of the world and asked followers to make efforts to help those less fortunate, noting that Jesus Christ himself was born an impoverished outcast.
The midnight mass this year, due to coronavirus advice and restrictions, was held in the back of St. Peter's Basilica with only a small group in attendance. The event is typically held in the main section of the basilica and attracts thousands.