The refugees, who are thought to have Hungarian ancestry, are understood to have been welcomed into the country with the tacit support of the Orban administration and the help of the Hungarian Charity Service of the Order of Malta.
The news has come as a surprise in the conservative central European state, given the anti-immigration stances and refugee crackdowns of premier Viktor Orban.
“We are speaking about Hungarians and we do not consider Hungarians migrants,” Mr Orban’s chief of staff, Gergely Gulyas, told a press conference in response to the report.
Confirming that the programme began in April 2018, he added: “They, like any other Hungarian, have a right to return home.”
A controversial law passed by the Orban government last year restricted the activities of NGOs and charities that provide assistance to migrants. The law was de facto targeted at those groups helping people arriving by land from the Middle East and Africa.
The Hungarian opposition seized on the latest developments, claiming the government was acting hypocritically.
“We call on the government to register itself as an organisation supporting migration and to pay the tax,” said MEP Csaba Molnar from the liberal DK party at a press conference.
“Just to be clear: we have no problem with refugees and with welcoming them, we support that. What we object to is the government treating Hungarians like idiots, not least its own supporters.”
As well as its own domestic crackdowns, Hungary has been engaged in running battles with Brussels over whether it should have to take its share of migrants and refugees arriving in Europe from conflict zones.
The UN refugee agency UNHCR said late last year that at least three million people had left Venezuela, mostly on foot, because of the turmoil in the country. Neighbouring Colombia has taken one million refugees, Peru around 500,000, and Ecuador 220,000.
Several thousands of Hungarians are thought to have immigrated to Venezuela after the Second World War.
The charity, which is said by the Hungarian media to be providing plane tickets, housing and work permits, is declining media requests for comment on the programme, which is apparently operating with government support.
It says it will not comment on the matter because of the interests of the people involved – leading to speculation it does not want to cause a backlash against the scheme.
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