Rwandan President Paul Kagame has threatened to round up Catholic faithful who visit a global pilgrimage site in his country, accusing them of "worshipping poverty".

Every year thousands of people, many travelling for several days on foot, visit Kibeho, a town in southern Rwanda where the Virgin Mary is said to have appeared to three schoolgirls four decades ago.

But Kagame lashed out at the pilgrims after more than 20,000 attended a Catholic mass in the hillside town on Assumption Day, August 15.

In an address to a youth conference on Wednesday, he described the pilgrimage to Kibeho, where the three teenagers said the mother of Christ appeared to them in November 1981, as "horrible".

“I thought that when you pray, you are praying for what can help improve your lives, praying to get rich and get out of poverty," he said.

"No one must worship poverty. Do not ever do that again... If I ever hear about this again, that people travelled to go and worship poverty, I will bring trucks and round them up and imprison them, and only release them when the poverty mentality has left them," said Kagame, himself a Catholic.

It is not clear what prompted the outburst by Rwanda's iron-fisted ruler and the Catholic Church in the country has not yet made any public comment.

The 1981 event was authenticated by the Vatican in 2001 and the site has become a popular destination for Catholic pilgrims from all over the world, many hoping for miracles or cures for illness.

Local media reported earlier this month that the Catholic Church is seeking funding of Rwf3.5 billion ($3 million) to expand Kibeho.

Almost all Rwandans are Christians, with Catholics making up roughly half the population.