The proposed legislation would still allow abortions in cases where the mother's life is at risk or the pregnancy results from a crime. But it would ban abortions of irreparably sick or impaired foetuses and those with Down syndrome.
Thousands of people joined protests in Warsaw and other cities on Friday against the conservative government's latest attempt to restrict abortion.
Many voiced anger more broadly at the policies of the ruling Law and Justice party, which has been accused by domestic critics and international bodies of eroding democracy and civic freedoms.
"This is against attempts at taking away our right to decide what we want," said Paulina Rudnik, a 44-year-old lawyer at the Warsaw protest.
In the crowds around her, people held banners including "Free choice" and "A woman is a human being" and chanted slogans demanding reproductive freedom.
Poland has one of the strictest laws in Europe, allowing abortion only if the woman's life is at risk, the pregnancy is the result of rape or incest, or the foetus is damaged.
An attempt to ban all abortions in 2016 sparked mass nationwide protests by women dressed in black that forced the government to abandon the plan.
The proposed legislation would continue to allow abortions in cases where the mother's life is at risk or the pregnancy results from a crime. But it would ban abortions of irreparably damaged foetuses and those with Down syndrome.
In Warsaw, protesters gathered at the seat of the influential Roman Catholic bishops, who support further tightening of the law.
Beating drums and blowing horns, they marched to the parliament and then moved on to the headquarters of the ruling right-wing party, which houses the office of party leader Jaroslaw Kaczynski.
"I hope this protest has the same effect as the one in 2016. Forcing women to have babies is inhuman," Karolina Chelminska, 26, a graphic designer, said.
A protest of hundreds in Wroclaw included a sign reading: "I will not give birth to a dead baby."
The EU Commissioner for Human Rights Nils Muiznieks and UN experts are urging Parliament to reject the bill.
The proposal was brought by a civic organisation and is now at the commission stage in parliament.