"We will not shut up. We will not obey. Withdraw the bill immediately!" the around 3,000 protesters shouted amid claps and whistles as they marched to Kadikoy square on the city's Asian side.
Others waved banners emblazoned with slogans such as "#Rape cannot be legitimised" and "AKP, take your hands off my body," a reference to the ruling party of President Recep Tayyip Erdogan, which introduced the bill.
The opposition, celebrities, and even an association whose deputy chairman is Erdogan's daughter have expressed alarm over the move.
Justice Minister Bekir Bozdag on Saturday moved to reassure opponents that the bill would not pardon rapists.
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"The bill will certainly not bring amnesty to rapists.... This is a step taken to solve a problem in some parts of our country," he told a NATO meeting in Istanbul.
After the controversy, Prime Minister Binali Yildirim late yesterday ordered his ruling Justice and Development Party (AKP) to hold talks with the opposition in parliament on the planned measures.
"We will not allow the AKP to acquit and set free rapists in this country," one of the women protesters who gave her name as Ruya told AFP.
"Women will resist and take to the streets until this law and similar other laws are withdrawn."
Another protester, a middle-aged man named Ugur, was at the protest with his 14-year-old daughter.
"I am concerned about my daughter's future," Ugur told AFP. "AKP is passing any law they want in the parliament."
"That's the maximum we can do. To protest," he said.
If passed, the law would allow the release from prison of men guilty of assaulting a minor if the act was committed without "force, threat, or any other restriction on consent" and if the aggressor "marries the victim".
The legal age of consent in Turkey is 18 but child marriage is widespread, especially in the southeast.
Another protester, Yagmur, called the bill a "nonsense", saying that it was a trap to open the way to legitimise religious weddings -- common in some parts of the country.