Hungary is set to hold a government-sponsored referendum seeking support for rejecting any future EU plan to resettle migrants among member states.
An EU summit in Bratislava on Friday is set to discuss the migrant crisis, and next week the United Nations General Assembly is holding a high-level meeting on refugees and migrants.
Luxembourg's Foreign Minister, Jean Asselborn, is reported to have told German newspaper Die Welt that Hungary should be excluded from the EU for anti-migrant policies that undermine the bloc's values.
The direct call for the exclusion of a fellow EU member state is unprecedented.
It underscores the extent of Europe's divisions over sharing responsibility for the more than one million migrants and refugees who reached its shores last year.
Hungary's Foreign Minister, Peter Szijjarto, has accused his counterpart of seriously insulting his nation and its people.
"It seems to be that he's very frustrated about the current situation in Europe and he's very frustrated about the fact that he has excluded himself quite a long time ago from the politicians that can be taken seriously."
Hungary has been one of the loudest critics of EU plans to redistribute asylum-seekers among member states.
Last year, it built razor-wire fences on its borders with Serbia and Croatia to stem the flow.
In a referendum due on October 2, the government is seeking support to reject any future EU quotas stipulating how many refugees countries within the bloc should take.
Mr Szijjarto has defended the process, saying Hungarians should be given the opportunity to shape their nation's immigration policy.
"The Hungarian people now will have the opportunity as first people in European Union to make a decision about a really important question regarding the future of Europe. Unlike Jean Asselborn we listen to the voice of the people. This is what democracy is about."
The European Union's Foreign Policy Chief, Federica Mogherini, has told the European Parliament in Strasbourg the bloc's approach to the refugee crisis is feeding into the global response in a significant way.
And she says European countries need to accept that large movements of people are going to keep coming.
"This is I know something that some of our citizens don't like to hear. But this is the simple reality of today's world. In a world of seven billion people with rising inequalities, with dramatically diverse demographic trends, migration is the new norm."
She says if properly managed, migration could bring nations great opportunities.
"And we need to face also with a certain realism our own European demographic trends and realise that we need and we will continue to need migration. So, it's not something we need to stop."
The United Nations High Commissioner for Refugees, Filippo Grandi, has called for Europe to engage in a calm debate on the issue of refugees.
"There is a time now to have this rational discussion - beyond the politicisation of some of these issues, beyond the manipulation that some irresponsible politicians are carrying out, using this pretext to just gain votes."
Next week the United Nations General Assembly in New York will hold a high-level plenary meeting on refugees and migrants.
The High Commissioner says it is important the meeting examine ways to improve the way European nations integrate newcomers from countries including Syria, Iraq and Afghanistan.
"It is one of the challenges of the future. And it is also, if well done, a manner to counter xenophobic tendencies, violent rejection, propaganda against foreigners."
