Pope Leo, who became the first American to lead the Catholic Church earlier this month, has previously appeared to make veiled criticisms of Vance and the Trump administration's migration stance.
In February, an X account under Leo's name shared criticism of the White House's plans for mass deportations of migrants.
That same month, the account also shared a link to an opinion piece titled: "JD Vance is wrong: Jesus doesn't ask us to rank our love for others."
The Vatican has not responded to previous requests from BBC News to confirm whether the account belonged to Pope Leo.
On Sunday, Vance said the United States was "very proud" of the Chicago-born pontiff.
"Certainly our prayers go with him as he starts this very important work," the vice-president said.
