Hungary's ruling Fidesz party wants to draw up legislation to effectively close its southern borders to illegal migrants, a Fidesz politician said.
Prime Minister Viktor Orban has criticized European Union proposals for migrant quotas as "bordering on insanity".
The quotas were drafted in response to the thousands of deaths among asylum-seekers trying to reach Europe across the Mediterranean. The crisis has grown acute this year.
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.
Most asylum-seekers move on to other European Union member states but Germany and Austria have signaled that they were planning to send some 15,000 migrants back to Hungary.
He said that therefore, "urgent steps" needed to be taken.
"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.
Hungary borders Romania, Serbia and Croatia on the south. Serbia is not an EU member, and Croatia and Romania are not members of the EU's borderless Schengen zone.
Most asylum-seekers came to Hungary from Kosovo, Afghanistan and Syria last year.
Rogan did not say when Fidesz would draw up the legislation.
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.
The Hungarian government also launched a public campaign against illegal migrants last week, with billboards saying: "If you come to Hungary, you can't take away the jobs of Hungarians."
Fidesz has lost ground in polls to the far-right, anti-immigrant Jobbik party and analysts say that its moves against migrants were intended in part to halt that.