EU ministers are to meet and try to resolve a dispute over how to relocate 120,000 asylum seekers who have recently arrived in Europe.
A group of central European states is resisting calls for 22 EU members to accept mandatory quotas.
Hungary, which takes one of the strongest lines on the issue, has said European borders are under threat.
The arrival of hundreds of thousands of migrants has exposed deep divisions within the EU.
Home affairs ministers meeting in Brussels on Tuesday will be hoping to forge a consensus ahead of an emergency meeting of EU leaders on Wednesday.
After talks on Monday between Hungary, Poland, Slovakia and the Czech Republic, all of whom oppose quotas, Czech Foreign Minister Lubomir Zaoralek insisted the four were still "absolutely dedicated" to finding a solution.
If disagreements persist, ministers could force a deal through by a majority vote, rather than a unanimous decision.
If they choose to do so, home affairs ministers can approve a mandatory quota scheme by a qualified majority rather than by unanimous decision.
Enough countries are in favour of the proposal to form a majority - but huge efforts are still being made to find a compromise.
Such have been the divisions of the last few days that an unprecedented majority vote on an issue like this, involving national sovereignty, would be quite a gamble.
Still, there is pressure on the home affairs ministers to make a firm decision before EU leaders gather on Wednesday.
The leaders can only take decisions on a unanimous basis, and they are keen to focus on longer term issues like border security and extra help for countries in the Middle East that have borne the brunt of the Syrian refugee crisis.
Hungary has granted its army extra powers to deal with migrants, allowing them to use rubber bullets, tear gas and net guns.
Migrants, said Hungarian Prime Minister Victor Orban, "are over-running us".
"They're not just banging on the door, they're breaking the doors down on top of us. Our borders are under threat. Hungary is under threat and so is the whole of Europe."
His tough stance has drawn sharp criticism from other European colleagues.
At a temporary camp in Opatovac, Croatia - another key transit country for migrants - angry scenes broke out early on Monday evening.
A BBC team there saw riot police entering the camp at one point and said at least one person was injured.
Most of those travelling in the Balkans are seeking a route north to Germany and Scandinavia.
UN Secretary General Ban Ki-moon called for EU leaders to show compassion, saying he was concerned for the situation facing refugees and migrants arriving in Europe.
Greek Prime Minister Alexis Tsipras, newly sworn in after his re-election, said unless responsibility was shared "there is no point in talking about a united Europe".
His country has seen thousands of arrivals, many of them fleeing Syria's civil war, although less boats were reported Monday due to an incoming storm.
Croatia is to demand Greece stops moving on migrants to the rest of Europe at this week's meetings, Reuters reported.