Szydlo was responding to a Monday deadline set by the Commission for Poland to reverse a controversial overhaul of the country's top court that has set off a fiery dispute between Warsaw and Brussels.
"Poland will never succumb to any ultimatum," Szydlo told parliament. "There are some in the European Commission... Who want to destroy the European Union rather than see it develop."
The European Union's executive arm warned earlier this week it could take further action against Poland because of concerns over its commitment to the rule of law.
The exact contents of the opinion are not known, but if Warsaw fails to address the issues raised, it could eventually face a suspension of voting rights in the European council of ministers, the EU's most important decision-making body.
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Szydlo's government, led by the populist Law and Justice (PiS) party, plunged Poland into political crisis in December when it pushed through legislation to revamp the constitutional court and modify its decision-making rules.
Since taking office in November, the government has pushed through several pieces of controversial legislation, including strengthening state control over public broadcasters and seeking to tighten already limited access to abortions.
Earlier this month, around a quarter of a million Poles marched to defend their country's place in the European Union and protest against the PiS government.