Hungary's ruling Fidesz party wants to draw up legislation to effectively close its southern borders to illegal migrants.
Antal Rogan, the head of Fidesz' parliamentary group, said on Sunday that by the end of May, 50,000 migrants had crossed Hungary's borders illegally, compared with 43,000 in the whole of 2014.
"Fidesz' parliamentary faction is considering drawing up a bill and practically making a proposal to close the southern border with certain legal means," Rogan told Kossuth radio.
"In practice this would mean that we'd pass a law saying that those entering Hungary from a safe country, from a safe transit country, cannot apply for political asylum here."
Rogan said migrants' lives may have been in danger in Syria but they crossed Greece, Serbia or some other countries in the Balkans where they were already safe and could apply for asylum there.
This week the Hungarian government launched a public campaign against illegal migrants, with billboards saying: "If you come to Hungary, you can't take away the jobs of Hungarians."
Prime Minister Viktor Orban has criticised European Union proposals for migrant quotas as "bordering on insanity".
Most asylum-seekers came to Hungary from Kosovo, Afghanistan and Syria last year.
A UNHCR regional spokeswoman said that under international law, which Hungary had also signed up to, every individual had the right to file an asylum claim.
"I don't think it's worth getting into a debate about third countries or anything like that because in every case it's the facts of each individual that's important," Kitty McKinsey said.
A Danish rightwing party expected to hold the balance of power after an election later this month has endorsed a British-style referendum on EU membership, a position that could crack the pro-EU consensus of northern Europe's political elite.
An Irish aid worker has warned that tens of thousands of migrants are risking their lives in treacherous sea crossings because they have a greater chance of surviving than if they remained at home.