* Proposal designed to retaliate against U.S. Magnitsky Act
* Unclear whether the Kremlin will back the initiative (Adds Duma vote, Medvedev quotes, updates detentions)
By Alissa de Carbonnel and Sonia Elks
MOSCOW, Dec 19 (Reuters) - Russia's parliament initially approved a bill banning Americans from adopting Russian orphans on Wednesday in reprisal for a U.S. law punishing alleged Russian human rights violators in a row that has strained bilateral relations.
Despite criticism of the measure by Russian Foreign Minister Sergei Lavrov, pro-Kremlin lawmakers overwhelmingly voted for the proposal and for another that would bar Russian non-profit groups which receive funds from the United States.
Only 15 of 450 deputies in the lower house, the State Duma, opposed the proposals.
The bill, expected to pass its final reading on Friday, still needs President Vladimir Putin's signature to become law.
The Kremlin, worried about long-term damage to relations with Washington, distanced itself from the measure on Wednesday, raising doubts about whether Putin will sign off on it.
Putin's spokesman, Dmitry Peskov, described the lawmakers' initiative as "tough and emotional" and the Kremlin's position as more "restrained".
Nationalist politicians have long viewed foreign adoptions of Russian children as an embarrassment that implies Russia cannot care for its own, but critics of the bill say children should not fall victim of political manoeuvring.
Police said they detained 30 protesters for holding an unauthorised demonstration outside the Duma.
Some two dozen protesters stood in the freezing cold heckling deputies as they entered the building. One activist held up before-and-after pictures of a Russian child looking bruised, then happy with his new American parents.
"It deprives children of the possibility to grow up in families of loving parents," one protester, Natalya Tsymbalova, said shortly before she was detained.
"To deprive children of this possibility is mean."
The proposals were added to a bill which would bar entry to Americans who violate the rights of Russians abroad and freeze their assets, mirroring the so-called U.S. Magnitsky Act.
Putin backed the original bill but had signalled he wants to limit the spat with President Barack Obama's administration. The Kremlin says Obama will visit Russia early next year.
Russia is the third most popular country for U.S. foreign adoptions after China and Ethiopia, according to the U.S. State Department. Last year, 962 orphans were adopted by Americans.
It is a statistic bemoaned by Russian politicians. Prime Minister Dmitry Medvedev said Russians should not be adopted abroad - although he did not say whether he supported the bill.
"Foreign adoptions is a sign of ... our indifference," Medvedev said in televised comments on Wednesday.
On Tuesday, Foreign Minister Lavrov said a complete ban on U.S. adoptions would be wrong and Education Minister Dmitry Livanov criticised the idea on his Twitter micro blog.
Any ban on U.S. adoptions would go back on new rules agreed in July.
The U.S. Magnitsky Act, which infuriated Moscow, was drawn up because of concern over the death in a Russian prison of anti-corruption lawyer Sergei Magnitsky in 2009. It orders the United States to deny visas to Russian human rights violators.
In turn, the Duma's bill is named in honour of Dima Yakovlev - a Russian 2-year-old who died when his American adoptive father forgot him in a closed car in sweltering heat in 2008.
The man was acquitted in the United States, sparking public outraged in Russia and the stricter adoption rules. (Reporting by Sonia Elks and Maria Tsvetkova,; Writing by Alissa de Carbonnel,; Editing by Alistair Lyon)