The opposition, celebrities, and even an association whose deputy chairman is the daughter of President Recep Tayyip Erdogan expressed alarm over the move.
But the government insisted the legislation was aimed at dealing with the widespread custom of child marriages and the criticism was a crude distortion of its aim.
The measures were approved in an initial parliamentary reading on Thursday and will be voted on again in a second debate in the coming days.
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In an apparent bid to soften the controversy, Prime Minister Binali Yildirim later ordered the ruling Justice and Development Party (AKP), which introduced the bill, to hold talks with the opposition in parliament on the plan, a Turkish official 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.
Dozens protested the bill in central Istanbul, tearing up copies of the proposed legislation and brandishing slogans like "rape is a crime against humanity".
"Until she is 18, a child remains a child, that is why this has to be condemned," said protester Fadik Temizyurek.
- 'Pardons rape' -Celebrities waded into the debate, with prominent actress Nurgul Yesilcay tweeting that "what we are talking about is not being a woman in this country, or being a man, but staying a human being".
On Twitter, the hashtag #TecavuzMesrulastirilamaz (Rape Cannot be Legitimised) became a top-trending topic as users took to social media to express their anger.
"The AKP is pushing through a text which pardons those who marry the child that they raped," said an MP for the opposition Republican People's Party (CHP) Ozgur Ozel.
A petition on change.org urging the authorities to block the legislation has received over 600,000 signatures.
The pro-government Women's and Democracy Association (KADEM), whose deputy chairman is Erdogan's younger daughter Sumeyye Erdogan Bayraktar, said one of the biggest problems of the bill would be proving on a legal basis what constituted force or consent.
"How can the 'own will' of such a young girl be identified?" it asked. "We would like to draw attention to issues that might arise in case of it coming into force."
- 'Child marriage a reality' -Yildirim said the measure would only be applied once on past convictions, applying to offences committed before November 11, 2016.
"There are people who get married before reaching the legal age. They just don't know the law," he told reporters in Ankara, adding that the measure aims to "get rid of this injustice".
He said claims that the law would de-facto legalise rape were "completely false", accusing the CHP of exploiting the issue for political gain.
Justice Minister Bekir Bozdag said marriages involving minors were "unfortunately a reality" in Turkey but the men involved "were not rapists or sexual aggressors."
He said the measure would affect some 3,000 families.
The latest controversy comes after Turkey's constitutional court in July annulled a criminal code provision punishing as "sexual abuse" all sexual acts involving children under the age of 15.
Defenders of that law argued it made a distinction between cases of sexual acts involving a young teenager as opposed to a much younger child.
Campaigners accuse the government of not doing enough to stamp out the practice and of being more interested in pushing up the birth rate.
Gauri van Gulik, Amnesty International's Deputy Europe Director, said the parliament bill risks sending "the wrong message and could lead to further abuse."
"It is impossible... to guarantee that there was in fact full and informed consent of the girl, not just of her family," she said.
