Viktor Orban’s comments come as refugees are forced off train headed towards Austria and taken to refugee camp.
The UK is to accept thousands more refugees from camps based on the Syrian border following criticism that it has not been doing its share, British newspapers are reporting.
The reports said government officials were on Thursday working on a plan to bring in thousands more people, but not those already in Europe.
The Guardian reported that British Prime Minister David Cameron did not want to encourage more people to make the perilous journey across the Mediterranean Sea to reach the UK.
The move comes amid pressure on the British government from members of the public to end the refugee crisis that has seen thousands of people die trying to flee the war in Syria.
More than 260,000 people have signed a petition demanding that the government increase its assistance.
Under British law, only 100,000 signatures are needed to prompt a debate in parliament.
The petition went viral on social media sites Facebook and Twitter on Thursday after pictures emerged of a Syrian child lying lifeless on a Turkish beach on Wednesday.
The child, three-year-old Aylan Kurdi, drowned with his mother and five-year-old brother, while trying to make the journey between the Turkish resort of Bodrum and the Greek island of Kos.
The images sparked international outrage and demands from governments to do more to protect those trying to reach the EU.
In an interview with the BBC on Thursday,Cameron said he was “deeply moved” by the image of Aylan, adding the UK would fulfil its “moral responsibilities” towards refugees.
“Britain has always been a home to real asylum seekers, genuine refugees,” Cameron said.
Several members of Cameron’s Conservative party have called on the government to grant more refugees asylum.
“The UK I know has always shouldered its burden in the world…we can and must do more at home,” said Ruth Davidson, the leader of the party in Scotland.
The UK I know has always shouldered its burden in the world. DfID is doing life-saving work abroad but we can – & must – do more at home 1/2
— Ruth Davidson (@RuthDavidsonMSP) September 3, 2015
The British government says it has granted protection to nearly 5,000 Syrian refugees since the start of the civil war.
— Tim Montgomerie 🇬🇧 (@montie) September 3, 2015
Cameron was criticised on social media for previous comments he has made about people wanting to enter the UK. In July he called those wanting to get in to the country a “swarm”.
Writing in the Independent newspaper, commentator Yasmin Alibhai-Brown slammed the prime minister for his use of the word, and other politicians for demonising refugees.
“Our Government can only talk in numbers, so too most of the media…social psychopathy is the result. “
Others compared the British prime minister’s reaction to that of his German counterpart, Angela Merkel, who has promised to accept 800,000 refugees.
The refugee crisis is Europe’s biggest since World War II. Thousands of Syrian refugees and others, including from Iraq, Afghanistan and Sub-Saharan countries, have made the journey to EU states or are attempting to do so.