The State Department had warned last week that such a law could have "repercussions" on Poland's relationship with the United States.
"The United States is disappointed that the president of Poland has signed legislation that would impose criminal penalties for attributing Nazi crimes to the Polish state," Secretary of State Rex Tillerson said in a statement.
The law is intended to safeguard Poland's image abroad but instead has set off an unprecedented diplomatic row with the United States and Israel.
Duda said the law will now go before Poland's Constitutional Tribunal for a ruling on whether it conforms with free speech guarantees.
"Enactment of this law adversely affects freedom of speech and academic inquiry," Tillerson said.
Tillerson referred to Poland as "our strong ally," and acknowledged that terms like "Polish death camps" were "painful and misleading." But he said fundamental freedoms must be protected in combatting historical inaccuracies.
"We believe that open debate, scholarship, and education are the best means of countering misleading speech," he said.
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