The SOS was sent by an asylum-seeker, one of 14 relocated from a refugee camp earmarked for closure near Budapest to what they say are freezing military tents in Kormend close to the Austrian border.
Nemeth, the Catholic parish priest in Kormend, a town of around 12,000 souls some 230 kilometres west of Budapest, quickly offered them shelter in the parish community hall.
"I'm not a hero, it was simply my duty as a committed Christian to help," the bespectacled and portly 61-year-old told AFP in the parish house next door where he lives.
In 2015 Orban built fences on Hungary's borders to keep out migrants, and changed laws enabling the expulsion and jailing of "illegal border crossers".
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Refugee camps are being closed while a government referendum in October urged Hungarians to vote "No" to the EU's plan to relocate migrants around the bloc. The ballot however was declared invalid because of low voter turnout.
"Hungary doesn't need a single migrant," Orban has said, warning that the "poison" of mass migration will destroy Europe's Christian identity.
"I follow Jesus, not the state's leaders," he told AFP, citing a passage from the Bible: "For I was hungry and you gave me something to eat... I was a stranger and you invited me in."
The priest says his inspiration is Pope Francis who has regularly defended migrants and called on Europe to keep its doors open to those in need.
Upstairs in the parish hall, priest vestments hang on racks at one end, while mattresses and rucksacks line the walls.
The group of young men, all awaiting decisions on appeals of rejected asylum claims, is comprised of Iraqi Kurds, Afghans, Cameroonians, Nigerians, Cubans and a Congolese. They include both Christians and Muslims.