By Matt Spetalnick and Mark Hosenball

WASHINGTON (Reuters) - Secretary of State John Kerry on Sunday laid out what he said was overwhelming evidence of Russian complicity in the downing of a Malaysian airliner in eastern Ukraine as he made the U.S. case against Moscow in the most emphatic and explicit terms yet.

Delivering his points in a blitz of U.S. morning news shows, Kerry demanded that Russia take responsibility for actions of allied separatists suspected of shooting down the passenger plane and he expressed disgust over the rebels' "grotesque" mishandling of victims' bodies at the crash site.

Kerry threatened further sanctions against Moscow and called on European partners, who have lagged behind Washington in imposing penalties over the Ukraine crisis, to take Thursday's plane downing as a "wake-up call" to get tougher with Russia. He also raised the prospect of increased assistance to Ukraine's embattled pro-Western government.

But despite the angry rhetoric, Kerry offered no specific new plans to force Russian President Vladimir Putin, accused by the West of trying to destabilize Ukraine, to back down.

President Barack Obama's Republican critics responded by accusing the administration of being too restrained and called for broader "sectoral" sanctions on Russia's energy and banking industries, something Washington has avoided so far because of the potential damage to the European and global economies.

Kerry's words added to a chorus of outrage from Western powers over the downing of Malaysia Airlines flight MH17, which killed all 298 people on board, and the subsequent problems gaining access to the crash site in an area of eastern Ukraine controlled by pro-Russian rebels.

While stopping short of placing direct blame on Moscow, Kerry put forth the most detailed U.S. accusations so far, based on the latest U.S. intelligence assessments. He said that Russia provided pro-Moscow insurgents with the sophisticated anti-aircraft systems used to down the plane.

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He said the United States has seen major supplies moving into Ukraine from Russia in the last month, including a 150-vehicle convoy of armored personnel carriers, tanks and rocket launchers transferred to the separatists several weeks ago.

He also said the United States intercepted conversations about the transfer to separatists of the Russian SA-11 radar-guided SA11 missile system it blames for the plane downing.

U.S. authorities have seen a video of a missile launcher - with a least one rocket missing from its battery - moving back into Russia from a rebel-held area, Kerry said.

"There's (an) enormous amount of evidence, even more evidence that I just documented, that points to the involvement of Russia in providing these systems, training the people on them," Kerry said on CBS's "Face the Nation."

Moscow denies involvement and has accused the Ukrainian military in the shootdown.

A U.S. official familiar with Washington's assessments of the incident said Russia was believed to have decided to reinforce the rebels with more advanced weaponry because of concern that Ukrainian government forces had been making gains.

RUSSIA AND THE SEPARATISTS

Kerry laid out the evidence of a Russian connection that tracked closely with an official unclassified U.S. intelligence summary released over the weekend. It said intelligence analysts confirmed the authenticity of an audiotaped conversation provided to the press by Ukrainian authorities of a known separatist leader boasting of downing the plane.

"We also have information indicating that Russia is providing training to separatist fighters at a facility in southwest Russia" that includes missile systems, it said.

The plane downing is widely seen a potential turning point in the Ukraine crisis that has taken relations between Russia and the West to a post-Cold War low. Kerry, who spoke to his Russian counterpart, Sergei Lavrov, by phone on Saturday, called on Moscow to use its influence and publicly seek responsible action from the separatists, including access to the crash site.

"It is clear that Russia supports the separatists, supplies the separatists, encourages the separatists, trains the separatists. And Russia needs to step up and make a difference here," Kerry said on NBC's "Meet the Press" program.

He said foreign investigators have been given only limited access to the crash site. "Drunken separatists have been piling bodies into trucks and removing them from the site ... What's happening is really grotesque and it is contrary to everything President Putin and Russia said they would do."

U.S. officials have expressed hope that European anger over the plane downing would help unify the 28-member EU bloc, which stands to lose more by punishing Russia since it does 10 times more trade with Russia than the United States does.

Kerry challenged the Europeans to become assertive. "It would help enormously if some countries in Europe that have been a little reluctant to move would now recognize this wake-up call and join the United States and President Obama in taking the lead, and also stepping up," he said.

ALL OPTIONS 'ON THE TABLE'

American lawmakers also called on Putin to take action, with Democratic Senator Dianne Feinstein saying on CNN, "Putin, you have to man up."

Kerry's sharpened charges against Moscow suggest that Washington could move faster to expand its sanctions. But the consensus in Washington is the next phase, if it comes, will involve further surgical targeting of Russian oligarchs and others close to Putin, not sweeping curbs on entire sectors.

"The president is prepared to take additional steps," Kerry told Fox News. "We are discussing with the Ukrainians right now what they need, what else we can do." He said all options were "on the table" except sending in U.S. troops.

South Carolina Republican Senator Lindsey Graham said on NBC that Washington should arm Ukraine "so they can defend themselves." Obama has been wary of creating a proxy war.

(Additional reporting by Doina Chiacu, Jim Loney, Ayesha Rascoe, Jason Lange; Editing by Doina Chiacu, Frances Kerry and Lisa Shumaker)