The FTSE 100, France's CAC 40 and the German DAX all eked out a gain, led by miners and banks. But consumer stocks weighed on major benchmarks.
Will Hedden, sales trader at IG Index told CNBC it was hard to read too much into the markets given the low volumes. But he said U.S. Treasury Secretary Timothy Geithner's warning on Wednesday that the U.S. would hit its debt ceiling on Monday, December 31 would weigh on stocks.
"This is going to make trading even more reserved than we had expected it," he said.
European markets which were closed for the Boxing Day holiday on Wednesday are playing catch up with other markets on Thursday.
Asian stocks rose on Thursday on hopes of a deal on the U.S. fiscal situation, with Japanese stocks hitting a 21-month high as a weaker yen helped exporters. Safe havens such as gold and Treasurys have also been gaining as investors hedge their bets on the "fiscal cliff".
In key European news, Bankia shareholders may face big losses after Spain's bank rescue fund said on Wednesday that the company had a negative valuation of 4.2 billion euros.
Shares in Bankia fell 12.5 percent at the opening of the stock market on Thursday.
In Italy, outgoing Prime Minister Mario Monti was gaining the support of a number of centrist politicians, according to a report in the Financial Times, setting the stage for a confrontation with former Prime Minister Silvio Berlusconi in elections set for February 24 and 25.