Duda said that the bill will be reviewed by a top Polish court to assess the possibility of adding amendments in the future.
It has caused a diplomatic crisis with Israel, which fears it will enable Poland to whitewash the role of Poles who killed or denounced Jews to Germans during the German occupation of Poland during World War II.
Andrzej Duda said in a televised address the legislation would safeguard Poland's worldwide reputation, but Israel called for amendments, saying the two countries had a "joint responsibility" to preserve the memory of the Holocaust.
Israel's Foreign Ministry said Tuesday that it would continue to communicate with Poland despite its reservations about the law.
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The bill has drawn criticism from the United States and condemnation from a number of global organisations as well as Polish minority groups. This weekend, Beate Mazurek, a spokesperson for Poland's ruling Law and Justice Party (PiS), quoted a tweet by a Catholic priest exclaiming that criticism of the law by Israel's ambassador to Poland, "make it hard for me to look at Jews with sympathy and kindness".
"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.
"Israel and Poland hold a joint responsibility to research and preserve the History of the Holocaust". The idea seemed to have been dropped, but made a sudden reappearance when the lower house of parliament approved a bill on January 26, the eve of International Holocaust Remembrance Day.
While "Polish" is nearly always used as a geographic description in that context, Poles feel the phrase cruelly portrays their country as having been in charge of the Nazi-run camps, while in fact Poles made up the largest group of victims after Jews.
At least 1.9 million non-Jewish Polish citizens were killed by the Nazis as well.
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"The blood of Polish Jews cries from the ground, and no law will silence it", Bennett said Monday.
Before World War II, Jews made up 10 percent of Poland's population.
"No legislation will change the past", Bennett said.
"It is an undeniable historical truth that many Poles helped murder Jews, providing information about them to the Nazis, handing them over, or murdering them themselves", said Education Minister Naftali Bennett.
Defending the law, Duda said it would not prohibit Holocaust survivors and witnesses from talking about crimes committed by individual Poles.
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The leaders of Ukrainian, Tartar, Jewish and other groups said in a letter published by the Polish Press Agency late Saturday they especially oppose recent "numerous and loud manifestations of anti-Semitism".