Religious freedom and cooperation between church and state were also discussed at the meeting, with US Secretary of State Marco Rubio also taking part.
A statement continued: "Finally, there was an exchange of views on current international issues with a shared call for respect for humanitarian and international law in conflict zones, and support for negotiated solutions among the parties involved."
The papal audience lasted 45 minutes, Vance's spokesperson said. It took place behind closed doors without reporters present.
The Vatican said Vance also held positive talks with Archbishop Paul Richard Gallagher, who is responsible for the Holy See's diplomatic relations.
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