Pope Leo and new Archbishop of Canterbury Sarah Mullally met for the first time on Monday, in a symbolic encounter at the Vatican in which the leaders of the long-separated Catholic Church and Church of England exchanged gifts and prayed together.

Mullally, the first woman to serve as spiritual leader of the world’s 85 million Anglicans, was ‌welcomed by Leo, the first US leader of the world’s 1.4 billion Catholics, into his formal office at the Vatican’s ornate apostolic palace.

The two, who...