Financial markets remained volatile Thursday, a day after concerns over the U.S. fiscal situation combined with renewed worries over the European economy to hammer stocks.

For most of the day, a vote by the Greek Parliament to back another round of austerity measures had helped shore up confidence. However, as U.S. trading gathered pace, the previous day's despondency appeared to settle over markets once again.

"Volatility will likely continue to be the name of the game going forwards as markets lurch from one crisis to the next and investors will continue to trade with extreme caution," said Mike McCudden, head of derivatives at Interactive Investor.

In Europe, the FTSE 100 index of leading British shares was down 0.3 percent at 5,776 while Germany's DAX fell 0.5 percent to 7,197. The CAC-40 in France was 0.1 percent higher at 3,412.

In the U.S., the Dow Jones industrial average was down 0.3 percent at 12,893 while the broader S&P 500 index fell 0.3 percent to 1,390.

For once, the monthly press conference from Mario Draghi, the president of the European Central Bank, proved to be a non-event — at least among investors. His warning that the economic outlook for the 17 countries that use the euro remains weak in spite of a calmer feel in bond markets was not much of a surprise. Draghi spoke after the bank's governing council left its key interest rate unchanged at the record low of 0.75 percent.

Investors in the U.S. are also focusing on developments in Washington as politicians return to the nation's capital following the general election.

Top of re-elected President Barack Obama's in-tray is to fashion a deal with the Republicans who maintained their control of the House of Representatives. Their leader, Speaker John Boehner, said in brief remarks Wednesday that he may be ready to bargain.

An agreement is needed if the U.S. is to avoid the so-called fiscal cliff — a combination of higher taxes and government spending cuts that automatically take effect unless Congress agrees on a new budget by Jan. 1. Economists warn that a failure to reach a concrete decision will push the world's largest economy back into recession.

"A compromise between the Democrats and Republicans to avert next year's fiscal cliff may not be reached until the eleventh hour," said John Higgins, an analyst at Capital Economics.

Moody's and Fitch have both warned that the U.S.'s triple A credit rating may come under threat if a deal isn't forthcoming. Last year, rival Standard & Poor's stripped the U.S. of its top-tier rating amid the political infighting in Washington.

"The hope is that politicians will be more inclined to be flexible given they don't have to worry about being re-elected for quite some time yet," said Michael Hewson, markets analyst at CMC Markets.

Despite worries over the fiscal cliff, the dollar garnered support on Wednesday through its perceived status as a haven at a time of financial distress. That remained, albeit modestly, Thursday, with the euro trading 0.2 percent lower at $1.2730.

Earlier in Asia, markets tumbled, tracked their counterparts in Europe and the U.S. the day before. Japan's Nikkei 225 index shed 1.5 percent to close at 8,837.15, while Hong Kong's Hang Seng sank 2.4 percent to 21,566.91.

In mainland China, the Shanghai Composite Index lost 1.6 percent to 2,071.51, while the Shenzhen Composite Index lost 2.3 percent to 831.71.

On Thursday, China's weeklong Communist Party congress began — the once-in-a-decade forum to name China's top leadership. Markets are looking for hints on how the new leadership plans to tackle the nation's economic slowdown.

In the oil markets, benchmark oil for December delivery was up 51 cents to $84.95 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell $4.27 amid the turmoil on Wednesday.