Pope Francis met Hungary's nationalist Prime Minister Viktor Orban on Thursday, expressing appreciation for Budapest taking in Ukrainian refugees, and Orban invited the pope to make a state visit to Hungary.

Orban, on his first international visit since winning a fourth consecutive landslide election victory this month, spoke to the pope privately for about 40 minutes in the pontiff's library in the Vatican's Apostolic Palace. 

The Vatican said there would be no statement because the visit was a private one. 

A video released by Vatican television showed the pope giving Orban a medal of St. Martin of Tours, a fourth century French saint who was born in what is today Hungary.

According to legend, St. Martin cut his cloak in half and shared it with a beggar.

"I chose this for you ... I thought of you Hungarians who are now receiving the refugees," Francis said.

The U.N. refugee agency says the number of people fleeing Ukraine to escape Russia's invasion has passed 5 million in Europe's worst refugee crisis since the end of World War Two.

About 625,000 refugees have arrived in Hungary since the start of the war and about 80% of them have moved on, according to the latest figures from the Hungarian government.

State news agency MTI quoted Orban as saying the pope "encouraged us that we shouldn't give up this good habit of ours," referring to taking in refugees.

Orban and the pope have previously differed on immigration policy in Europe.

On his way to Slovakia last September, Francis stopped in Budapest for seven hours to close a Church congress in the Hungarian capital.

Orban said he invited the pope to visit Hungary next year and received an "encouragingly positive answer," according to MTI.    

At the end of Thursday's private audience, Francis was heard telling Orban: "God bless you, you family and Hungary." Orban responded: "We are waiting for you".