The amendment removes fines or criminal penalties of up to three years in prison for anyone found guilty of ascribing Nazi crimes to the Polish nation or state.
Lawmakers in Poland's right-wing dominated lower house of parliament voted 388 in favour of the amendment, with 25 against and five abstentions.
The Senate is expected to adopt the amendment later on Wednesday before it is signed into law by the president.
Poland's right-wing Prime Minister Mateusz Morawiecki proposed the changes out of the blue earlier on Wednesday, telling MPs that the criminal penalties had "stirred so much controversy they began to be counterproductive."
The law, passed by Poland's Senate in February made it a criminal offense to ascribe "responsibility or co-responsibility to the Polish nation or state for crimes committed by the German Third Reich".
The main aim of the legislation was to prevent people from describing Nazi German death camps in Poland, such as Auschwitz-Birkenau, as Polish.
But the jail terms included in the law ignited an unprecedented diplomatic row with Israel and demands for the recall of Israel's ambassador in Warsaw.
Israel expressed deep concern that the legislation could open the door to prosecuting Holocaust survivors for their testimony should it concern the involvement of individual Poles for allegedly killing or giving up Jews to the Germans.
Israel also saw it as a bid to deny the participation of individual Poles in killing Jews or handing them over to the Nazis.
Poland's government faced international criticism over the law, which it insists was meant to protect Poland from false accusations of complicity in the Holocaust.
Poland was occupied by Nazi Germany in World War II, losing six million of its citizens, including three million Jews.
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