Activists picketed the Duma to oppose the bill. An online petition against it has attracted more than 200,000 signatures.
Olga Batalina, one of the bill's co-authors, rejected suggestions that the bill would grant impunity to abusive partners.
"The Criminal Code still carries criminal responsibility for battery, but now it will be applicable only for repeat offenders," she told state television. All those "who terrorise their family members, who do it repeatedly will face criminal responsibility".
Nearly 38,000 people, almost three quarters of them women, suffered assault by a family member in 2013, according to Russia's interior ministry.
Women's rights campaigners say the real number of victims is likely significantly higher, partly because many do not report it. Several rights groups are now pushing for a separate federal law that would specifically address domestic violence.
The amendment will have to pass a third reading in the Duma and be approved by the upper house and president Vladimir Putin before it becomes law.
The second reading was the last chance to amend the bill before it lands on Putin's desk.
A survey by VTsIOM, a state-run pollster, this month found that 19 per cent of Russians said "it can be acceptable" to hit one's wife, husband or child "in certain circumstances".
Where to get help:
If it is an emergency and you or someone you know is at risk, call 111.
• Women's Refuge: 0800 733 843
• Victim Support: 0800 842 846
• Lifeline: (09) 522 2999
• Family Violence Info Line: 0800 456 450
This story was originally published in the Daily Telegraph.