* Tens of thousands join rival pro-Kremlin and anti-war demos in Moscow
* Rallies comes a day before referendum on Crimea joining Russia
* Most Russians back President Putin's policy in Ukraine
By Maria Tsvetkova and Jason Bush
MOSCOW, March 15 (Reuters) - Russia saw the largest opposition protest in almost two years in Moscow on Saturday, as Muscovites took to the streets in their thousands to demonstrate both for and against President Vladimir Putin's policies in Ukraine.
Crimeans vote on Sunday on whether to reunite with Russia after pro-Russian forces took control of the peninsula, triggering the worst East-West confrontation since the Cold War.
Most Russians strongly back Putin's actions and see Crimea as rightfully part of Russia. But a minority are horrified, fearing that Putin is risking war with another Slavic country formerly seen as a brother nation.
Although smaller than protests that he faced after parliamentary elections in 2011, Saturday's anti-war rally, which witnesses said attracted around 30,000 people, is a sign that his intervention in Ukraine might provide a rallying point for an opposition movement that had run out of steam.
Since being re-elected president in 2012, Putin has worked to neutralise political opposition, mindful of the street protests that overthrew governments in Georgia and Ukraine in 2003 and 2004-5 - actions that help to explain his deep antipathy to the movement that toppled Ukraine's pro-Russian president, Viktor Yanukovich, last month.
On Sakharov Avenue, site of the first large anti-Putin rally in December 2011, when tens of thousands protested against electoral fraud, demonstrators waved Ukrainian and Russian flags as well as EU flags like those carried by pro-European demonstrators in Kiev's Maidan square.
The march appeared to be the largest opposition rally since June 2012, although police put the turnout at around 3,000.
"I am ashamed for Russia and our people," said publishing company employee Valentina Legonkova, 69, who was carrying a Ukrainian flag although she is Russian.
"We are behaving towards Ukraine like swine," she said. "We will soon be on the level of North Korea."
Some chanted "Glory to Ukraine, glory to the heroes!", a slogan also borrowed from Kiev, others "Down with Putin!", "No to war!", "No to fascism!" and "Russia without Putin!"
One placard read: "Hungary 1956, Czechoslovakia 1968, Ukraine 2014", likening Russia's actions to the Red Army's suppression of east European reform movements in the Cold War.
"My duty is to show support for the Ukrainian people in its desire to live independently from the dictatorship of the elder brother," said Moscow teacher Irina Seseikina.
The protest taps into a wider vein of discontent, strongest among the Moscow middle class, who are also appalled at rising corruption, political repression and censorship under Putin.
But so far, the Ukraine crisis and last month's spectacular Winter Olympics in Sochi have solidified broader support for Putin, whose increasingly nationalist and conservative agenda plays well among Russians nostalgic for the Soviet Union.
His approval rating now stands at about 70 percent. In a recent poll by the independent Levada Centre, two-thirds said they believed that not only Crimea but also mostly Russian-speaking eastern Ukraine were "in essence" Russian lands.
In the two weeks since he received parliamentary backing to deploy troops in Ukraine, Russia has seen dozens of government-backed rallies supporting the "defence" of Crimea, while smaller unsanctioned anti-war protests have led to scuffles with police and dozens of arrests.
The largely state-controlled media have pushed the Kremlin's view of the revolution in Ukraine as an anti-constitutional coup by fascist extremists with Western backing.
In a rally on Saturday organised by a Russian Orthodox movement "in support of Crimea and against fascism", 15,000 gathered on Revolution Square near the Kremlin, according to police.
Accompanied by a brass band playing patriotic marches, the well organised demonstrators, some waving Soviet hammers and sickles, chanted "Crimea is Russia", "We defend our own!" and "No to fascism!"
"We want to say a firm 'no' to the fascist junta that came to power in Kiev and therefore we naturally want to support our comrades in Ukraine," said Pyotr, one of the protesters.
Another pro-Kremlin demonstrator, Captain Alexei Ryabtsev, said: "Sevastopol means for Russia and for the Russians much more than the Falklands mean for England. But England didn't give the Falklands up and went into a big war, right?"
Few of the anti-war marchers believed that their action would make a difference.
"These images are for the evening news, which will talk about a (subversive) 'fifth column'," said Alexander, a teacher who declined to give his last name.