* World stocks find footing after vicious sell-off
* Euro hits 2-month low after ECB holds rates steady
* U.S., German government debt prices little changed
NEW YORK, Nov 8 (Reuters) - World stocks stabilized on Thursday on hopes the United States will tackle its deep fiscal problems to skirt a recession, while the euro fell to a two-month low after the European Central Bank refrained from taking more action despite signs of further economic slowdown.
A glimmer of investor confidence emerged that Washington may reach a deal to avoid the "fiscal cliff," a set of automatic tax hikes and spending cuts, which begin to kick in on Jan. 1.
Fears that a timely compromise was out of reach led to a massive sell-off in stocks, oil and risky assets on Wednesday, a day after U.S. President Barack Obama was re-elected and voters left the Congress divided.
"To the extent we start to see some clarification of what (Congress) is thinking about, whatever it may be, it will provide some confidence," said Rick Meckler, president of investment firm LibertyView Capital Management in Jersey City, New Jersey.
On Wall Street, the three major U.S. stock indexes dipped in late morning trade, reversing slight gain after a flat opening.
The Dow Jones industrial average slipped 21.54 points, or 0.17 percent, to 12,911.19. The Standard & Poor's 500 Index shed 1.92 points, or 0.14 percent, to 1,392.61. The Nasdaq Composite Index declined 3.90 points, or 0.13 percent, to 2,933.39.
The FTSE Eurofirst 300 index of top European shares was little changed at 1,097.97, holding steady after logging its biggest one-day drop in two weeks on Wednesday.
The MSCI world equity index was down 0.5 percent at 325.21 after Tokyo's Nikkei lost 1.5 percent.
Across the Atlantic, the ECB left key interest rate at 0.75 percent, disappointing some traders who had bet on more policy easing in the wake of recent comments by President Mario Draghi on the weak economic outlook and gloomy European Commission GDP estimates.
The absence of more ECB action spurred selling in the common currency, knocking it down to a two-month low versus the dollar at $1.2719. It last traded at $1.2739, down 0.25 percent for the day.
"The general theme here is that weak growth is weighing on the euro," said Steven Saywell, global head of FX strategy at BNP Paribas in London.
The euro had been under pressure before the ECB decision even though the Greek parliament approved in the early hours of Thursday an austerity package needed to unlock international aid and avert bankruptcy, defying political rifts and violent protests.
Meanwhile, Spain, another heavily indebted euro-zone member, sold 4.8 billion euros ($6 billion) of new debt, completing its cash needs for this year. This meant Madrid can hold out longer before asking for international aid.
The somewhat encouraging news in Europe curbed safe-haven bids for U.S. and German government debt.
The yield on the benchmark 10-year U.S. Treasury note held steady at 1.680 percent, while German Bund futures were up 16 basis points at 142.91.
In commodity markets, oil rose after tumbling more than $4 on Wednesday on concerns about weak demand for fuel as the U.S. and European economies face the risk of a protracted slowdown.
Brent crude traded 22 cents higher at $107.04 per barrel after falling nearly 4 percent on Wednesday, its steepest drop since December 2011.
U.S. crude rose 49 cents to $84.94, after losing nearly 5 percent in the previous session, also its biggest slump since December 2011.