The EU directive "applies in Poland and in this case it supersedes national law," Poland's top Muslim leader, Mufti Tomasz Miskiewicz, said, quoting an expert legal analysis commissioned by the Muslim community and the meat industry.
Animal rights activists have hailed the ban, but Jewish and Muslim leaders in overwhelmingly Catholic Poland argue that it violates their religious freedom and Israel has called it "unacceptable".
Farmers and exporters of meat to Israel and Muslim countries, who exported up to 350 million euros ($460 million) worth of kosher and halal meat a year before the ban, have also condemned it.
The Jewish community has asked Poland's Constitutional Court to rule whether the ban violates their religious freedom, but Miskiewicz said there was "no need" for such a ruling because European law trumped the ban.
The ancient practices of Muslim halal and Jewish kosher slaughter are therefore "legal in Poland since January 1 and can be conducted in slaughterhouses," he told reporters in Warsaw.
European Union rules on the slaughter of livestock are designed to minimise the animals' suffering, but religious groups are exempted from a requirement that animals be stunned before death.
Under kosher and halal rules, animals are killed by slitting their throats.
This method was banned in Poland on January 1 after the Constitutional Court deemed it incompatible with animal rights legislation.
Then on July 12, lawmakers struck down a government bill that would have reinstated the practice, spurring cheers from animal rights activists and criticism from religious leaders and commercial butchers.
Miskiewicz forwarded the expert legal analysis on Tuesday to Poland's agriculture ministry with a request that it cancel all ministerial directives banning slaughterhouses from performing halal and kosher slaughter within seven days.
"We're approaching the Feast of the Sacrifice (Eid al-Adha) on October 15, the most important Muslim religious feast, and we're counting on being able to celebrate it in line with our traditions," he said.
The Jewish and Muslim communities each number around 20,000 to 30,000 in Poland, a country of some 38 million.