By Doug Palmer

WASHINGTON (Reuters) - The U.S. House of Representatives voted overwhelmingly on Friday to "name and shame" Russian human rights violators as part of a broader bill to drop Cold War-era trade restrictions, brushing off warnings from Moscow that the move would damage relations.

The House voted 365-43 to approve the legislation, which takes a jab at the policies of Russian President Vladimir Putin while ensuring U.S. companies get the full benefits of Russia's entry into the World Trade Organization on August 22.

"Since Vladimir Putin was re-elected president in May 2012, his government has taken a harsh and confrontational approach to ongoing protests, cracking down on the Russian people's growing discontent with corruption and creeping authoritarianism," said Democratic U.S. Representative Jim McGovern.

The bill, which still needs Senate approval, would establish "permanent normal trade relations," or PNTR, with Russia while directing President Barack Obama to publish the names of Russians believed involved in the abuse and death of Sergei Magnitsky, a Russian anti-corruption lawyer who died in 2009 in a Russian jail.

It also would require the Obama administration to deny visas and freeze the assets of any individual on the list, as well as other human rights violators in Russia on an ongoing basis.

Russia has vowed a "tough" response to the legislation, which it views an intrusion into its affairs.

Deputy Foreign Minister Sergei Ryabkov said earlier on Friday that Russia has already prepared its next steps but gave no details. Other Russian officials have indicated that Moscow would retaliate by imposing sanctions on U.S. officials it accused of violating Russian citizens' rights.

They would be likely to include officials involved in refusing a Russian request for the extradition of a convicted arms trader, Viktor Bout, serving a 25-year prison term in the United States.

U.S. action turns next to the Senate, where some supporters are pressing for a broader version of the legislation that would allow the United States to impose sanctions on human rights violators anywhere. No vote has been set in the Senate.

Obama is expected to sign the bill if it reaches his desk, even though the White House initially pressed for PNTR legislation without the human rights sanctions provisions.

(Additional reporting by Thomas Grove in Moscow; Editing by Will Dunham)