Critics have said that the bill, which would allow the release from jail of men convicted of assaulting underage girls if they marry their victims, risks legitimising rape.
At the weekend, thousands rallied against the bill in Istanbul, urging the government to withdraw the proposals.
"This (bill) does not in any way cover rape crimes... This is not forgiveness, it is only a legal amendment," Deputy Prime Minister Numan Kurtulmus said in televised comments after a cabinet meeting.
But he said the main opposition Republican People's Party (CHP) and Nationalist Movement Party (MHP) could suggest changes ahead of a second vote on Tuesday.
"If the MHP or CHP have other proposals regarding this case, we state clearly that we are open to evaluating those proposals," Kurtulmus added.
Justice Minister Bekir Bozdag has 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 bill is due to be voted on again on Tuesday after it was approved in an initial parliamentary reading on Thursday.
If it is passed, it would permit 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".
Prime Minister Binali Yildirim said last week that the claims it would de-facto legalise rape were "completely false" and the measure would only be applied once to past offences committed before November 11, 2016.
On Monday, the UN children's agency UNICEF together with three other UN agencies said if the bill was passed in its current form, it would weaken Turkey's ability to fight against child marriage and sexual abuse.
