On the currency market the euro was stable at $1.3165 at 1500 GMT against 1.3161 late Monday.
The yen failed to benefit from signals the government is ready to step into forex markets again to block its rise, with the Japanese unit strengthening to 82.00 against the dollar against 83.78 the evening before.
In Paris, the CAC 40 was off 0.09 per cent at 3,858.72 points, while in Frankfurt the DAX finished up 0.02 per cent at 6,972.10 points.
The London Stock Exchange was closed for a public holiday.
Early gains in Paris were wiped out by the release of disappointing US data showing housing prices falling faster and the consumer confidence index dropped in December to 52.5 points from 54.3 points the previous month.
Natixis bank analysts said "real estate remains the black mark on economic recovery underway in the United States".
Together with the drop in consumer confidence the reports weighed on investor sentiment regarding the recovery of the US labour market, they said.
Telecom equipment maker Alcatel-Lucent advanced 1.76 per cent on Tuesday, however, after agreeing to pay $137 million in fines and penalties to settle US charges it paid bribes to win contracts in Latin America and Asia.
But trading was thin in the holiday week, with market turnover was just 800 million euros, a fourth of normal trading sessions.
In Frankfurt, the DAX managed to stay in positive territory, but the auto sector continued to slide on fears of increased regulations and taxes in China, an increasingly important market for German car makers.
Daimler dipped 0.14 per cent, Volkswagen dropped 0.62 per cent and BMW fell 1.64 per cent. On Monday each of them lost more than 4.0 per cent.
Last week the city of Beijing said it planned to cut new car registrations by two-thirds to ease its massive traffic jams.
On Tuesday the Chinese government announced it plans to increase the purchase tax for small cars next year, as part of a winding back of stimulus measures introduced to combat the global financial crisis.
French car makers Renault lost 0.67 per cent and Peugeot dropped 0.56 per cent.
Elsewhere in Europe, Brussels slid 0.19 per cent, Lisbon dropped 0.22 per cent, and Milan fell 0.32 per cent. Swiss shares ended flat, while Madrid gained 0.05 per cent, and Amsterdam rose 0.32 per cent.
On Wall Street, stocks indices also dropped following the release of the US housing and consumer confidence data, but the Dow managed to claw its way back into positive territory.
At 1730 GMT the Dow Jones Industrial Average was up 0.05 per cent at 11,561.08.
The tech-rich NASDAQ fell 0..29 per cent to 2,659.64.
The broader S&P 500 index was off 0.03 per cent at 1,257.16.
Societe Generale analyst Olivier Korber said meanwhile that on the currency market "all is calm, with investors taking no positions as they await the end of the year."
In European trading on Tuesday the euro changed hands at $1.3165 against $1.3161 late in New York on Monday, at 107.95 yen (108.98), 0.8555 pounds (0.8535) and 1.2515 Swiss francs (1.2641).
The dollar stood at 82.00 yen (82.78) and 0.9507 Swiss francs (0.9599).
The pound was at $1.5388(1.5417).
Asian stock markets closed mostly lower on Tuesday as traders returned to the Hong Kong bourse for the first time since China raised interest rates on Christmas Day.
Tokyo ended lower on the back of a strengthening yen but investors were broadly ignoring a batch of economic data showing Japanese consumer prices have been slipping every month for almost two years.
Hong Kong shed 0.93 per cent and Shanghai dropped 1.74 per cent.
What the stars mean:
★ Poor ★ ★ Promising ★★★ Good ★★★★ Very good ★★★★★ Exceptional