The Turkish government said the bill is not intended to pardon rapists, but to address underage marriage.
The law would allow the release of men who assaulted a minor "without force" and later married the victim.
The controversial bill has already sparked protests across the country.
However, the bill faces opposition from both public and political opposition, and may be withdrawn or changed before the vote in parliament.
In its current form, the bill applies to men who had sexual relations with girls under the age of 18. It allows the indefinite postponement of sentences for sexual abuse committed "without force, threat or trick".
The government said the aim was to exonerate men imprisoned for marrying an underage girl, apparently with her or her family's consent.
Marriage under the age of 18 is illegal in Turkey, but is practised in some parts of the large, predominantly Muslim country.
However, critics say that children cannot give consent, especially in a male-dominated culture, and the bill legitimises rape.
On Saturday, about 3,000 protesters gathered in Istanbul to oppose the legislation.
Protesters clapped and chanted: "We will not shut up. We will not obey. Withdraw the bill immediately!"
"A rape can't be justified," protester Fadik Temizyurek told the BBC.
"What does it mean to ask a child if they're OK? Until they're 18, a child remains a child, that is why this has to be condemned. We are here so that this law can't pass."
The bill follows a previous controversy after Turkey's constitutional court in July annulled part of the criminal code which classified all sexual acts with children under 15 as sexual abuse.
The UN children's fund has said it is "deeply concerned" about the bill.
"These abject forms of violence against children are crimes which should be punished as such, and in all cases the best interest of the child should prevail," said spokesman Christophe Boulierac.
Men who had sex with underage girls could have their convictions overturned if they marry their victims, under a bill due before Turkey's parliament on Tuesday.