(Updates throughout with Bush speech)

By Tabassum Zakaria and Jan Lopatka

PRAGUE, June 5 (Reuters) - U.S. President George W. Bush sought to calm Russia's Vladimir Putin on Tuesday over plans for a U.S. missile defence shield in Eastern Europe, saying on the eve of a big-power summit that Russia had nothing to fear.

But Bush also accused Russia of retreating on democracy.

Putin has reacted furiously to a U.S. plan for a radar system in the Czech Republic and missile interceptors in Poland, and warned Russia will target its missiles on Europe, as it did in the Cold War, if Washington proceeds.

Bush, in Prague ahead of a Group of Eight (G8) summit in Germany where he will meet Putin on Thursday, said the missile shield was intended to protect against threats from "rogue" regimes. He again called on Moscow to participate in its development.

"Russia's not our enemy," Bush said after meeting Czech leaders at the 9th century Prague Castle.

The increased tensions between Russia and the United States on the eve of the G8 gathering in Heiligendamm prompted concerns among U.S. allies.

"We consider it very significant that President Bush pledged to do all he can to explain these things to Russia and President Putin," Czech President Vaclav Klaus said.

Bush sought to dispel concerns that countries cooperating with the United States on the missile shield would be caught up in tensions with Russia.

"The Cold War is over. It ended. The people of the Czech Republic don't have to choose between being a friend of the United States or a friend with Russia, you can be both," Bush said.

Apart from seeing Putin at the June 6-8 summit, Bush has invited the Russian leader to his family's retreat in Maine next month.

Bush said his message to Putin at those meetings would be: "You shouldn't fear a missile defence system. As a matter of fact why don't you cooperate with us on a missile defence system, why don't you participate with the United States?"

Highlighting U.S. closeness with countries that Moscow considers to be part of its traditional sphere of influence, Bush will stop in Poland after the summit, followed by Albania and Bulgaria.

ON DEMOCRACY

Bush criticised Russia and China at a pro-democracy conference organised by former Czech president Vaclav Havel and ex-Soviet dissident Natan Sharansky in the room where the agreement officially dissolving the Warsaw Pact was signed.

"In Russia, reforms that once promised to empower citizens have been derailed, with troubling implications for democratic development," Bush said.

He criticised China for not doing enough on the political front. "China's leaders believe that they can continue to open the nation's economy without opening its political system. We disagree," Bush said.

But despite disagreements, Bush said the United States has "strong working relationships" and a "complex friendship" with those two countries and would continue to build on those ties.

"America can maintain a friendship and push a nation toward democracy at the same time," he said.

After the speech, Bush met with 30 pro-democracy activists, including Garry Kasparov, the champion chess player, who has called Russia a "police state".

Bush said the United States was using its influence to urge Egypt, Saudi Arabia and Pakistan -- allies in fighting terrorism -- to open up their political systems.

"Yet they have a great distance still to travel," he said.

Bush often says the removal of the Taliban from power in Afghanistan and Saddam Hussein as leader of Iraq allowed those countries to pursue democracy.

And while the Iraq war has become increasingly unpopular in America, Bush has stood firm against setting a timetable for withdrawing troops.

"Critics point to the violence in Afghanistan, or Iraq, or Lebanon as evidence that freedom leaves people less safe. But look who's causing the violence. It's the terrorists, it's the extremists," Bush said. "It is no coincidence that they are targeting young democracies in the Middle East." (Additional reporting by Caren Bohan)

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