But in a move that appeared created to soften the impact of his decision, President Andrzej Duda said he would also ask Poland's constitutional court to evaluate the bill - leaving open the possibility it would be amended.
The bill would set fines or a maximum three-year jail term for anyone who refers to Nazi German death camps as Polish.
"We are also concerned about the repercussions this draft legislation, if enacted, could have on Poland's strategic interests and relationships", she said.
"The blood of Polish Jews cries from the ground, and no law will silence it", Naftali Bennett said in a statement late Monday. Unusually, however, he said the bill would be reviewed by the country's Constitutional Tribunal.
"The government of Poland canceled my visit, because I mentioned the crimes of its people".
"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 said it still hoped Poland would make amendments. "Israel and Poland hold a joint responsibility to research and preserve the history of the Holocaust", the Israeli government said in a statement on Twitter.
While Duda said he would sign the bill, it was unclear when he is planning to do so and when it will become enshrined in law.
Poland is governed by a nationalist party, Law and Justice (PiS), which is keen to show the world how Poland was ruthlessly victimised by its German and Soviet neighbours in the war. Jews from across the continent were sent to be killed at death camps built and operated by Germans in Poland, including Auschwitz, Treblinka, Belzec and Sobibor. Bennett was supposed to head this week to Poland to meet the Polish Deputy Prime Minister Jaroslaw Gowin.
"I think that the bill is precise and does not require a change".
Moreover, whilst the concentration camps were the site where Jewish people were killed in the millions, the murdering of Poles of Christian and other denominations (numbering in the hundreds of thousands) should not be discounted or forgotten.
Before the outbreak of World War II, Jews lived in Poland for centuries, thriving in some eras and even becoming the world's largest Jewish population at one point. There are things that have been said and done on both sides - including by Israeli politicians who said that there were Polish camps - which haven't been helpful.
According to Czaputowicz, critical comments made by Israeli Prime Minister Benjamin Netanyahu about the Polish bill were "due to a misunderstanding". Polish people don't bear responsibility for the Holocaust, as such.
Relations between the two countries have been greatly strained by the Polish government's decision to push forward with the legislation. I accepted an invitation to a dialogue based on truth.