"The mechanism actually contributes to enabling Greece and Italy to deal with the impact of the 2015 migration crisis and is proportionate".
The group's European Union office director, Iverna McGowan, said Wednesday that "Slovakia and Hungary have tried to dodge the EU's system for solidarity, but each country has a role to play in protecting people fleeing violence and persecution".
Since compulsory quotas were introduced in September 2015, Hungary has not accepted a single asylum seeker, while almost 28,000 people have been relocated under the scheme, far below the 160,000 target.
Their case was supported by Poland, where a right-wing government has come to power since the 2015 deal.
Why didn't Hungary and Slovakia want to take in the asylum seekers?
Western EU states, including Germany, which took in the vast majority of the people who made it into the bloc and which will holds a parliamentary election on September 24, say the easterners can not be exempted from showing solidarity.
Hungary has not accepted a single asylum seeker since the measures were introduced two years ago. Slovakia and the Czech Republic have only taken in a handful.
They also say that opening their borders to refugees from migrants from war-torn countries such as Syria could leave them open to the threat of terrorism.
The Commission's chief spokesman, however, denied a report that the executive would propose a new round of 40,000 relocations.
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"ECJ confirms relocation scheme valid".
'It is time to be united and show full solidarity, ' Mr Avramopoulos said.
"It is right to clarify questions legally if there is doubt".
Gabriel added: "We can also expect now, and we do expect, that all European partners will keep to the verdict and implement the decisions without further hesitation".
In its ruling Wednesday, the court rejected all the arguments brought by Hungary and Slovakia.
Slovakia prime minister Robert Fico said his government "fully respects the court's decision" but added that the quotas were "politically wrong".
Hungarian Foreign Minister Peter Szijjarto said "politics has raped European law and values" in response to Wednesday's ruling.
Under worldwide and European law, countries are required to grant asylum to people fleeing war or persecution but not those classed as economic migrants, the EU designation for most sub-Saharan Africans.
The UNHCR urged European Union nations to "increase the pace of relocation for eligible asylum-seekers from Italy and Greece, and to fully meet their relocation commitments as a concrete gesture of solidarity towards countries of first arrival in the EU".