Earlier this year Prime Minister Mateusz Morawiecki tweeted that "Auschwitz-Birkenau is not a Polish name, and Arbeit Macht Frei is not a Polish phrase".
The change in the law was intended to distance the Polish people from any suggestion of culpability.
But the move has provoked an international outcry, particularly in Israel and the USA.
In February Mr Morawiecki said the outcry showed the world was biased against Poland.
However, he has now called on the lower house of parliament to remove the imposed jail terms from the bill, as politicians begin debating the issue today.
“We resign from the criminal provisions,” the head of prime minister’s office, Michal Dworczyk, told public radio.
The government said that following a public debate on the bill, it had decided that there were other “tools” it could use to “protect Poland’s good name”.
In April, a fringe nationalist group asked prosecutors to investigate if Israeli President Reuven Rivlin broke the law during a speech in Poland.
