Pope Francis on Wednesday spoke out against "denier" cardinals who refused the coronavirus vaccine, in an apparent swipe at his main opponent who recently contracted Covid-19.

"In the College of Cardinals, there are a few deniers. One of them, the poor man, contracted the virus," the pontiff told reporters as he flew home from a trip to Slovakia.

The 84-year-old did not name the man he was referring to, but conservative US Cardinal Raymond Burke, one of Francis' fiercest and most vocal critics in the Catholic Church, was recently admitted to hospital in the United States with Covid-19.

The pope said that in the heart of the Vatican, "everyone is vaccinated, with the exception of a small group".

"We are studying how to help them," he said during a press conference onboard the papal plane.

The pope is a strong advocate of coronavirus vaccines and has previously expressed his incomprehension with those who refuse to take it.

The pope is a strong advocate of coronavirus vaccines and has previously expressed his incomprehension with those who refuse to take it
The pope is a strong advocate of coronavirus vaccines and has previously expressed his incomprehension with those who refuse to take it POOL / Tiziana FABI

"It's a bit strange because humanity has a history of friendship with vaccines," Francis said, highlighting the jabs that have for decades protected children against measles or polio.

"We should clarify things and speak calmly," he advised, while also conceding that the debates over the different anti-coronavirus vaccines could create uncertainty or fear.

The pope made a brief stopover in Budapest on Sunday before visiting Slovakia, and held a private meeting with Hungarian Prime Minister Viktor Orban.

He is at odds with the populist leader's hardline stance on migration, but said Wednesday they did not discuss the issue.

Hungarian President Janos Ader did most of the talking during the three-way meeting, the pope said, and they focused on ecology as well as Hungary's support for couples hoping to have children.

For his part, Orban -- who has claimed Europe is threatened by a Muslim "invasion" -- said on Facebook that he had asked the pope in their meeting "not to let Christian Hungary perish".

During his press conference, the pope repeated his call for Europe to return to the principles of solidarity on which it was founded, warning of "the danger that it has become just a managerial office. And that is not good."