By Sonia Elks and Steve Gutterman
MOSCOW (Reuters) - Thousands of people marched through Moscow on Saturday in an orderly show of support for a ban on adoptions of Russian children by Americans, echoing President Vladimir Putin's demands for better care for Russian orphans in their homeland.
Carrying signs with slogans including "Children are our future" and "America - hands off our children", activists mixed bitter criticism of the United States with calls for improvements in Russia's own care system.
"These children are ours. We shouldn't give them away," said Natalya Bakhinova, 56, walking in one of two columns led by marching bands that converged in Moscow's Pushkin Square.
Police said 12,000 people joined the rally, and organizers denied allegations some were coerced or paid to attend.
Moscow has seized on the death of Russian-born three-year-old Max Shatto - who died in January in Texas, where his adoptive parents live - as justification for the ban that has increased tensions with the United States.
After improvements under a "reset" President Barack Obama initiated in 2009, ties have been strained by Syria and issues including Putin's charges of U.S. meddling and his treatment of opponents since he returned to Russia's presidency last May.
Activists on Saturday called for Max Shatto's younger brother Kris to be taken from the family and returned to Russia.
A few held photos of Max Shatto, bearing his Russian name Maxim Kuzmin, and of other Russian-born children who have died in the care of their adoptive American parents.
"We gave away something that is ours, and we need to take it back," said demonstrator Alexei Dobrenkov, 40.
Some Russian officials have suggested Max Shatto died as a result of abuse and lawmakers appealed to U.S. Congress last month to help return Kris, born Kirill Kuzmin, to Russia.
Texas authorities ruled the death an accident on Friday, saying he died from a torn abdominal artery and had bruises consistent with injuring himself.
The U.S. authorities said investigations into allegations of child abuse and neglect would continue and the priority was to ensure the safety of Kris Shatto, who remained in the adoptive family's home in Gardendale, Texas.
A Russian Foreign Ministry statement on Saturday expressed "concern" about the Texas authorities' findings and said it assumed they were only preliminary.
Demonstrators in Moscow echoed the official sentiment.
"That's nonsense - there is no way he could have killed himself," said Sergei, 57, who would not give his last name. "Too many of our children have died in America."
Russian officials say there have been at least 20 such deaths in two decades and that U.S. authorities have been too lenient on the parents.
More than 650,000 children are considered orphans in Russia, and 110,000 of them lived in state institutions in 2011, official data shows. There were about 7,400 adoptions by Russian families in 2011, versus 3,400 adoptions by families abroad.
Americans have adopted more than 60,000 Russian children since the collapse of the Soviet Union in 1991, surpassing parents from any other nation, but now only a few dozen children whose adoptions were approved before January 1 will be able to go.
Russia tacked the adoption ban onto legislation it passed in December in response to the U.S. Magnitsky Act, which bars Russians linked to the 2009 death of an anti-corruption lawyer other alleged rights abuses from entering the United States.
Tens of thousands of people, some labeling Putin a "child-killer", protested the adoption ban at a rally in Moscow in January billed as a "march against scoundrels".
Putin, who has stepped up efforts to instill patriotism during his new six-year term, has suggested the ban is justified because Russia should take care of its own children, and has ordered improvements to care for orphans.
Critics say the Russian system is plagued by neglect and instances of abuse, and accuse the Kremlin and lawmakers of using particularly vulnerable children as political pawns.
(Writing by Steve Gutterman)