Europe Shares Close Near 2012 Highs

European shares ended higher on Tuesday, with a key index closing just a few points below its 2012 high, as investors bet that U.S. Democrats and Republicans will reach a deal to avoid a "fiscal cliff" of year-end austerity measures.

Hopes of a U.S. budget deal rose in Washington on Tuesday, after U.S. House of Representatives Speaker John Boehner emerged from a meeting with fellow Republicans pledging to press forward on talks to avert a deadlock.

The FTSEurofirst 300 index of top European shares provisionally closed 0.6 percent higher at 1,138.82 points, less than 3 points shy of its 2012 high of 1,141.32 points hit last week.

The FTSE closed provisionally up 0.6 percent, the German Dax closed up 0.7 percent and the French CAC closed up 0.5 percent.

Cyclical shares featured among the biggest gainers, with Rio Tinto up 2.9 percent and Anglo American up 2.5 percent, while banks also rallied, with UBS up 1.9 percent and Banco Santander up 2 percent.

"The rally continues, without volatility. Markets are becoming complacent and every little dip is being bought. It feels like 2007," FXCM analyst Nicolas Cheron said.

The Euro STOXX 50 Volatility Index, Europe's widely-used measure of investor risk aversion, sank to a five-year low of 15.64 on Tuesday.

Still, worries about the euro zone remain on investors' minds. According to an EU report, Greece's economy could shrink by more than 4.2 percent in 2013, pushing the country into its sixth straight year of recession. The report by Greece's lenders at the European Commission, European Central Bank and International Monetary Fund warned that Greece, which received 34 billion euros ($44.7 billion) in aid this week, is likely to encounter more economic pitfalls and political resistance to the bailout program.