Russia is moving towards banning "baby boxes" - the hatches introduced in many countries where desperate mothers can safely abandon an unwanted infant.
But there has been sharp criticism of the ban proposed by senator Elena Mizulina and backed by the government.
Some warn that a ban will mean more dead babies left in woods or at rubbish dumps. Russia has about 20 of the boxes, where a mother can anonymously leave a baby at a maternity unit.
A UN committee has condemned the boxes.
In a report on Russia in 2014, the UN Committee on the Rights of the Child urged Russia to "undertake all the measures necessary to not allow baby boxes and to promote alternatives".
The Russian state, it said, should "address the root causes that lead to the abandonment of infants, including by providing family planning services and adequate counselling and social support for unplanned pregnancies".
The draft law - yet to be debated in parliament - would not only ban the boxes but also impose a fine of up to 5m roubles (£60,815; $79,000) for installing such a box. An organisation breaking the ban could be shut down for three months.
Russia's popular daily Komsomolskaya Pravda says (in Russian) that since the boxes first appeared in Russia in 2011 they have saved the lives of about 50 unwanted babies.
Ms Mizulina however argued that the boxes' existence encouraged struggling mothers to abandon their babies and risked fuelling the criminal trade in babies.
Anti-abortion campaign
The row about baby boxes coincides with a campaign to restrict abortion rights in Russia. An anti-abortion petition signed by the head of the Russian Orthodox Church, Patriarch Kirill, calls for abortions to be removed from the national health insurance system.
A leading Russian gynaecologist, Lyubov Yerofeeva, told BBC Russian that the anti-abortion initiative would pose a health risk to women who could not afford private fees. Some 90% of abortions in Russia are carried out in state clinics, "which shows that our women don't have the money for it", she said.
Baby boxes are also controversial in some other countries where they have been introduced. Germany, Switzerland, Italy, Canada, the US and Japan are just some of the countries that have them.
They have a long history. In the Middle Ages convents and churches had wooden cylinders built into their walls, where a destitute mother could leave an unwanted baby. To remain anonymous, the mother could simply ring a bell and walk away - and her baby would be collected by rotating the cylinder.
Supporters of the boxes in Russia deplored Ms Mizulina's proposal on social media.
"Bans will solve nothing. After banning abortions and baby boxes the number of underground abortions will grow, as well as children abandoned at rubbish dumps, left to die," wrote one user on the Russian blogging platform LiveJournal.
"First, baby boxes get banned. Next abortions will be banned. Then contraceptives. Back to the Middle Ages!" said the spoof account Fake-MIDRF on Twitter.