By Gabriela Baczynska

MOSCOW (Reuters) - President Vladimir Putin's adviser on child rights on Thursday flatly dismissed protesters' calls to rescind a ban on adoptions of Russian orphans by Americans, saying it puts an end to abuse and trading in Russian children in the United States.

Tens of thousands of people protested in Moscow on Sunday against Kremlin-backed legislation rushed through parliament to retaliate against the Magnitsky Act, a U.S. law which imposes sanctions on Russians accused of human rights abuses.

"What has been done ... will not be undone no matter what protests occur. This should be clear," Pavel Astakhov told a news conference, referring to the ban that came into effect on January 1.

He pointed to the overwhelming approval the law won in parliament before Putin signed it on December 28, adding to tension with the United States and drawing irate protests from critics who say it will compound the suffering of Russian orphans.

More than 650,000 children are considered orphans in Russia and about 110,000 of them lived in state institutions in 2011. They are only eligible for foreign adoption if repeated attempts to find them a home within the country fail.

Americans have adopted more than 60,000 Russian children since the Soviet collapse in 1991, according to the U.S. State Department. From 2000-2010, the figure was above 1,000 every year, with a high of nearly 6,000 in 2004.

Campaigners say most orphans with disabilities never find parents in Russia, making Americans or other foreigners the best hope for escape from Russia's troubled state children's homes.

But Astakhov said that of 3,400 Russian children adopted by foreigners in 2011, only about 5 percent were disabled.

ABUSE ALLEGATIONS

In approving the law, Russian lawmakers pointed to the deaths of 19 Russian-born children adopted by Americans in the past decade, and to what they see as overly lenient treatment of those parents by U.S. courts.

Defending the ban, Astakhov gave a detailed description of alleged sexual abuse of a Russian-born child by its adoptive American parents and said "child brokers" were trading Russian children in the United States.

"There are not that many countries left in the world today that export their children, let alone sell them," he said. Foreign adoption agencies "are involved in (child) trade," he said.

U.S. adoptions of children from Russia's sparsely populated east, where some Russians fear encroachment by China, were aggravating Russia's demographic problems, he said.

"Why is the Far East (of Russia) so popular? Think about that for a second. The Far East, where the population halved in 15 years. And still they are carrying children away from there in great numbers," he said.

Astakhov reiterated assurances that couples whose adoptions won final court approval before the law took effect will be able to take their adopted children home to the United States.

But several such American couples have been stuck in legal limbo because they are not being allowed to do that.

One of them, Rebecca and Brian Preece from Idaho, on Thursday waited outside the building where Astakhov's news conference took place, but he refused to meet them.

A court on Tuesday refused to hand to the Preeces the necessary documents for 4-year-old Gabriel, a boy with Down Syndrome they had adopted.

"We went to visit Gabriel yesterday. He was asking us when we are all going to drive away in a car," Rebecca Preece said, shivering in Moscow's winter chill as she waited for Astakhov. (Editing by Louise Ireland and Steve Gutterman)