(REUTERS) - The euro rallied and the dollar fell on Tuesday as better-than-expected economic data boosted appetite for risk, though the euro is likely to be pressured in 2012 on worries of high sovereign debt and low growth in the Eurozone.

Sentiment was boosted by better Chinese manufacturing and service data, while German unemployment fell more than forecast and Monday's manufacturing PMI showed less contraction than expected.

Traders reported demand for euros from U.S. and UK banks, which also contributed to its recovery from an 11-year low against the yen touched the previous day.

But persistent worries about high sovereign debt levels and a lack of policy solutions to a crisis now in its third year - which threatens to push the region's economy into recession - were expected to keep the euro under pressure.

The dollar is broadly weaker as risk assets begin the year in the black, with sentiment boosted by better-than-expected data releases in Europe and Asia, said Mark McCormick, currency strategist at Brown Brothers Harriman in New York.

The euro rose 0.7 percent higher on the day to $1.3022, pulling away from its 2011 trough of $1.2858 hit last week on trading platform EBS.

There needs to be a sustained improvement in euro zone fundamentals for a prolonged rebound in the euro, said Valentin Marinov, currency strategist at Citi in London. Concerns over Spain and Italy are still there and the risks from Greece are likely to continue to cloud the euro outlook, outweighing the positives coming from resilient German data.

Traders said stops in the euro were triggered through $1.3020 en route to the day's high around $1.3059, before it trimmed gains, its upside capped by offers reported from around $1.3050 through $1.3080.

Against the yen, the euro rose 0.6 percent to 99.98 yen. It fell to 98.71 yen in holiday-thinned trade on Monday, its lowest since 2000.

Investors are particularly concerned over Italy as it faces about 100 billion euros of bond redemption and coupon payments in the first four months of 2012, with 10-year borrowing costs near the crucial 7-percent level.

Worries over Greece were reinforced after a government spokesman said the country would have to leave the euro zone if it failed to clinch a deal on a second, 130 billion-euro bailout with its international lenders.

EU SUMMIT IN FOCUS

The euro may also get a reprieve if European policymakers make progress on steps to tackle the debt crisis in a series of meetings in January.

French President Nicolas Sarkozy will meet German Chancellor Angela Merkel in Berlin on January 9 for talks that are likely to center on new rules to enforce budget discipline across the European Union.

Finance ministers from the EU's 27 members will meet on January 23 before their leaders hold a summit a week later.

The Aussie rose 1.2 percent versus the greenback to $1.0341.

U.S. economic data will be a focal point for this week, starting with the ISM manufacturing survey on Tuesday.

The dollar dipped 0.1 percent to 76.77 yen, not that far from the record low of 75.311 yen hit in late October on EBS.