Slovenia has introduced new border restrictions for migrants as part of efforts to close the Balkans route from Greece to Western Europe.
Only migrants who plan to seek asylum in the country, or those with clear humanitarian needs will be allowed entry.
In reaction, Serbia said it would close its borders with Macedonia and Bulgaria to those without valid documents.
The future of the EU's passport-free Schengen zone is already in doubt.
Eight of its members, including Austria, Hungary and Slovakia, have tightened border controls, leaving thousands of migrants stranded in Greece.
Europe is facing its biggest refugee crisis since World War Two. Last year, more than a million people entered the EU illegally by boat. Most of them were Syrian, fleeing the country's civil war.
Slovenia, which is a EU member, has been used as a transit country by migrants trying to reach Germany and other northern European states.
But Slovenian Prime Minister Miro Cerar said on Tuesday the Balkan route was now effectively "shutting down".
He said the restrictions, which came into force at midnight local time (2300 GMT), were part of a wider initiative which would see other Balkan countries, as well as Greece and with the cooperation of Turkey, turn back "all irregular migrants".
The EU and Turkey are considering a radical plan including proposals to return all migrants arriving in Greece sent back to Turkey. For each Syrian sent back, a Syrian in Turkey would be resettled in the EU.
The UN expressed concern at the plan on Tuesday, while Amnesty International called it a death blow to the right to seek asylum.
Speaking to the BBC, Thorbjorn Jagland, Secretary General of the Council of Europe, said the proposal to send migrants back would contravene international law.
The deal, discussed at a summit in Brussels on Monday, has not been finalised and talks will continue ahead of an EU meeting on 17-18 March.
European leaders are billing their new proposal to deal with the refugee and migrant influx as a "game-changer", but the scheme is not agreed yet and there are doubts about whether it it is practical or even legal.
The centrepiece is a plan to take any refugees and migrants who cross the sea to Greece in smugglers' boats and return them, directly, to Turkey.
EU officials say whatever is finally agreed "will comply with both European and international law". Privately, though, some admit that, while the assessment of their lawyers is "quite promising", there are legal hurdles that must be overcome.
After Slovenia announced new restrictions, Serbia's interior ministry said it would act accordingly.
It said it had been informed that Slovenia would not receive migrants without valid visas and passports.
"Bearing in mind that the new regime is implemented by a member of the European Union, Serbia cannot afford to become a collection centre for refugees," it said in a statement.
It said Serbia, which is not a member of the EU or the Schengen agreement, would "harmonise all measures with the European Union and apply them reciprocally in its southern and eastern borders".
Under the EU's Dublin Regulation, asylum seekers to lodge claims in their EU country of arrival. However the bloc is said to be considering adopting a centralised system for processing applications instead.
More than 2,000 migrants, mostly from Syria, Iraq and Afghanistan, continue to arrive daily in Greece from Turkey.
Some 14,000 migrants are stranded around Idomeni on Greece's border with Macedonia after Macedonia closed its border to almost all.
What's in the EU-Turkey proposal?
The EU heads said "bold moves" were needed, and made the following proposals:
All new irregular migrants crossing from Turkey to Greece will be returned to Turkey. Irregular migrants means all those outside normal transit procedures, ie without documentation.
In exchange for every returned Syrian, one Syrian from Turkey will be resettled in the EU
Plans to ease access to the EU for Turkish citizens will be speeded up, with a view to allowing visa-free travel by June
EU payment of €3bn ($3.3bn; £2.2bn) promised in October will be speeded up, with the possibility of further aid to help Turkey deal with the crisis. Turkey reportedly asked for the sum to be doubled
Preparations will be made for opening new chapters in talks on EU membership for Turkey
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