In a statement afterwards, Gore said he asked the pontiff to launch a formal inquiry into the group.
The Vatican press office said the Pope wanted to have the meeting to listen first-hand to Gore's allegations.
While the Pope meets with a range of people daily, it is unusual for him to have a private meeting with a journalist.
Opus Dei ("Work of God") was founded in 1928 by a Spanish priest and teaches Catholics to strive for holiness through their work.
Most of its members are not clerics but maintain strict spiritual practices and often choose to remain celibate.
The group is known for close ties with the Vatican, where many employees are members including at least two former directors of the Vatican's press office.
Among allegations in the book, Gore said the group practices emotional control over its members and uses its influence to perpetrate financial fraud.
The organisation has sharply rejected Gore's accusations, saying in a 2024 statement that his book was "littered with twisted facts".
It did not immediately respond to a request for comment about the Pope's meeting on Monday.
Opus Dei has a strong presence in Peru, where Leo served as a missionary for decades before becoming pontiff.
The group says its mission is to spread Christian teachings across the world.
