No refugees have been accepted by Hungary or Poland, which saw the conservative Law and Justice party take power after October 2015 elections.
The United Nations on Wednesday praised a ruling by the European Union's top court that rejected a challenge by Hungary and Slovakia to relocation quotas approved at the height of the migrant crisis in 2015.
"The court dismissed the lawsuits filed by Slovakia and Hungary against the provisional mechanism for the mandatory distribution of asylum seekers (among European Union member States - ed.)", - reads the statement of the court following the hearing.
The mechanism helps frontier countries like Greece and Italy to deal with the impact of the 2015 migration crisis, and the European Union court said the action was proportionate.
In the suit, the two countries protested against the decision passed by the EU Council amid the peak of the migration crisis in 2015, introducing a quota mechanism to help relocated refugees from Greece and Italy.
So far less than 28,000 people have been relocated in the face of opposition from several Eastern European countries notably Hungary, Slovakia and the Czech Republic. Slovakia and Hungary denounced the plan at the time, citing their heterogeneous population, with a largely single ethnic representation, as an extra burden in resettling refugees.
Szydlo says she isn't surprised by the court's decision, but that it "absolutely does not change the position of the Polish government with respect to migration policy".
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Hungary and Slovakia were only slated to take less than 2,000 migrants combined, but they have refused to abide by the decision.
While Hungary and Slovakia have now failed in their legal challenge to the policy, that doesn't fix the political problem.
European Home Affairs Commissioner Dimitris Avramopoulos had said he regretted how certain member states "continue to show no solidarity and to ignore our repeated calls to participate in this common effort".
Hungary asked Brussels last week to pay €400 million towards the cost of security at its frontiers, and Mr Szijjarto complained that "the European Commission is not funding border protection, but only the admission of illegal immigrants".
He said migrant arrivals in Greece from Turkey had dropped 97 percent since the deal in March past year, and that more than 8,800 Syrians in Turkey had now found homes in Europe. Of those, 19,200 were transferred from Greece and 8,212 from Italy.
Amnesty International welcomed the court's decision.
While Brussels expects previously non-compliant countries to accept refugees within weeks, Mr Szijjarto pre-empted a bitter stand-off by saying "all legal means" would be used to oppose the decision.