* Obama says NATO must face up to Russian "brute force"
* Russia should not dictate future of Ukraine
* Denies U.S. conspiring with fascists in Ukraine
By Steve Holland and Paul Taylor
BRUSSELS, March 26 (Reuters) - President Barack Obama jousted rhetorically with Vladimir Putin on Wednesday with a point-by-point rebuttal of the Russian president's rationale for his incursion into Ukraine.
Without mentioning Putin's name, Obama used a keynote speech in Brussels on U.S.-European relations to push back against many of the justifications, grievances and accusations used by the Russian leader for Moscow's annexation of Crimea.
Obama offered advice for Americans sceptical about why they should care about what happens in a distant part of the world. And he told NATO allies it was time to bolster an alliance many of whose members have cut defence spending since the Cold War ended, in the face of what he called Russia's "brute force".
To Republican critics who want him to be tougher, Obama said this: Now is not the time for bluster, this is not a Cold war rerun, and there are no easy answers nor a military solution.
His speech looked and felt at times like a mirror image of Putin's March 18 oration in the Kremlin's gilded St George's Hall announcing the annexation of Crimea. The U.S. president spoke in Brussels' art deco Beaux-Arts concert hall in front of the grand organ.
"Just because Russia has a deep history with Ukraine does not mean it should be able to dictate Ukraine's future. No amount of propaganda can make right something that the world knows is wrong," he said.
Obama, who has had hours of frustrating private phone calls with Putin during the crisis, rejected several arguments the Russian president has made about Ukraine.
It was wrong to compare Russia's intervention in Ukraine to the U.S.-led war in Iraq or NATO's military campaign to drive Serbian forces out of Kosovo, he said, since in both cases the United States and its allies withdrew from foreign soil, while Russia remains in Crimea.
He cited his own grandfather's service during World War Two to reject Putin's assertions of Western backing for alleged fascists, neo-Nazis and anti-Semites in Ukraine.
"It is absurd to suggest, as a steady drum beat of Russian voices do, that America is conspiring with fascists inside Ukraine, or failing to respect the Russian people. My grandfather served in Patton's Army, just as many of your fathers and grandfathers fought against fascism," he said.
The contrast between Obama's emphasis on the shared values of the Atlantic alliance and Putin's denunciation of what he called the double standards of the West was striking. The U.S. leader noted that Russia no longer had either a military bloc or an ideology.
MANY FLAGS OR ONE
While Obama spoke against a backdrop of the massed flags of European nations, a symbol of international unity, Putin's backdrop consisted only of Russia's blue-white-red horizontal tricolour flags.
The Russian leader had walked into the hall along a long red carpet through gilded doors opened by soldiers in dress uniform standing stiffly to attention. Obama walked on to a simple wooden stage on his own, with no military escort and only security men on the doors.
Addressing a ceremonial joint session of the Russian parliament with his government sitting in the front row, Putin was repeatedly interrupted by ovations, some of them standing, and punctuated by cheers and some tears.
A hand-picked audience of young European "opinion leaders" listened to Obama in polite silence, more concerned to record the event on their smartphones and iPads than to applaud. When he received an ovation at the end, Obama waved almost self-consciously a few times and walked offstage on his own.
Belgium's king and queen, prime minister and government ministers watched from box seats.
Putin's speech was full of Russia's historical grievances, accusations of humiliation of Russians in the break-up of the Soviet Union, and charges of Western hypocrisy and misbehaviour towards Russia.
Obama argued that since the Cold War's end, the West had built cultural and commercial ties with Russia not as a favour to Moscow but out of shared interests. The G7 became the G8, he said, and the two former adversaries had worked to reduce nuclear arms and contain Syria's chemical weapons.
"So the world has an interest in a strong and responsible Russia, not a weak one. And we want the Russian people to live in security, prosperity, and dignity like everyone else - proud of their own history. But that does not mean that Russia can run roughshod over its neighbours," Obama said. (Additional reporting by Jeff Mason; Editing by Giles Elgood)