In an article earlier this month, Pompeo said the Catholic Church was risking its "moral authority" by renewing an agreement with China regarding the appointment of bishops.
US President Donald Trump receives support from conservative religious movements, including conservative Catholic voters, some of whom think Pope Francis is too liberal.
Human rights groups say many Catholics in China are persecuted and driven underground for pledging allegiance to the Pope instead of an official Chinese Catholic association.
Despite this, in 2018 the Vatican made a deal with China to have some say over the appointment of Chinese bishops.
At the time Pope Francis said he hoped the deal "will allow the wounds of the past to be overcome" and bring about full Catholic unity in China.
The agreement is expected to be renewed next month in the face of opposition from some Catholics, including in the US.
In a speech on Wednesday in Rome, Pompeo called on the Vatican to defend religious freedom in China, saying "nowhere is religious freedom under assault more than in China."
The Vatican's two top diplomats, Secretary of State Cardinal Pietro Parolin and Foreign Minister Archbishop Paul Gallagher, said Pope Francis will not receive Pompeo.
The two politicians also described Pompeo's public criticism of the Pope as a surprise and Archbishop Gallagher commented that issues for discussion should be negotiated "privately"
Cardinal Parolin also said it is possible Pompeo's comments were designed to encourage Catholics to support Trump at the polls in November.
"Some have interpreted it this way - that the comments were above all for domestic political use. I don't have proof of this but certainly this is one way of looking at it," he suggested.
He added that the Vatican's deal with China is nothing to do with the US.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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