(Fixes lead paragraph)
* Core bond yields, shares fall in European trading session
* U.S. Federal Reserve statement due later
* Short-lived rouble rebound after Finance Ministry sells FX
* Greece vote also in focus
By Lionel Laurent
LONDON, Dec 17 (Reuters) - Fears of a full-blown crisis in Russia and oil's continued slide pushed investors to seek safety on Wednesday, buying core bonds and selling stocks while the rouble failed to halt its prolonged tumble.
With only days to go before the end of the trading year, investors were also looking ahead to the U.S. Federal Reserve's final statement of 2014, due at 1900 GMT. Analysts expect it to remove language pledging to wait a "considerable time" before raising U.S. interest rates.
German bund yields, which set the standard for euro zone borrowing costs, held near record lows reached on Tuesday, when U.S. 10-year T-note yields also plumbed fresh two-month lows.
While there appeared to be some initial respite for the Russian rouble on Wednesday after the finance ministry said it had begun selling foreign currency, the rebound was short-lived and the currency was down 1.3 percent against the dollar and 0.2 percent down against the euro.
The Russian economy remains in the grip of a "perfect storm" of low oil prices, looming recession and Western sanctions over the Ukraine crisis.
But the Fed loomed.
"It's fair to say that we are to a large degree on hold ... until we get a clear idea about what the Fed is actually going to do," said Simon Derrick, chief currency strategist at Bank of New York Mellon in London. "That matters ... most pertinently because of what it means for the oil price."
Oil prices held near multi-year lows of around $60 a barrel o, with Brent crude down 60 cents to $59.41. Although oil's slide this year was triggered primarily by a supply glut, fears of cooling demand have also weighed on prices and hit financial markets in recent weeks.
Russian shares were mixed with the dollar-denominated RTS index up 3.6 percent - the first daily gains after a nine-day losing streak - while the rouble-based peer MICEX traded 1.8 percent lower.
The focus was also on Greece, which holds the first of three potential rounds of a presidential vote later in the day that will determine whether the country is forced into snap elections and a new period of political turmoil.
Energy companies were among the worst performers on the stock market, with the pan-European FTSEurofirst 300 equity index down 0.8 percent and the MSCI All-Country World index down 0.3 percent near mid-October levels.
Stocks exposed to Russia and Eastern Europe have also taken a big hit as investors assess the possibility of capital controls or writedowns. Austria's Raiffeisen Bank was trading near all-time lows on Wednesday; Reuters reported it was looking to sell its Polish unit, according to sources.
"The attack this week on the rouble has been quite violent, and the market is now pricing in a recession in Russia next year," said Arnaud Scarpaci, fund manager at Montaigne Capital.
"A lot of European companies exposed to Russia are under pressure. It's better to avoid names such as Metro, Nokian and Societe Generale, at least until things stabilise in Russia." (Additional reporting by Jemima Kelly, BLaise Robinson, Emelia Sithole-Matarise Editing by Jeremy Gaunt)