* Unemployment rate rises to 10.7 pct in January
* Consumer inflation at 2.7 pct in February
BRUSSELS, March 1 (Reuters) - Euro zone joblessness rose to a new euro-era high while inflation was largely steady at the start of 2012, data showed on Thursday, leaving the European Central Bank to juggle the demands of a slowing economy and only mild pressure on prices.
A cold snap in Europe and rising oil prices were probably behind the slight rise in February consumer prices that took inflation for the euro zone to 2.7 percent, compared to 2.6 percent in January, figures from the EU's statistics office Eurostat showed.
The euro zone's economic slump has helped bring the prices of goods, fuel and food down from last year's peak of 3 percent, but oil prices hit record highs in euro terms this month and undermined inflation's downward trend.
That suggests the ECB is likely to put off any quick decision to take interest rates to below 1 percent for the first time and economists see the bank in "wait-and-see" mode.
The bank wants to keep inflation below, but close to 2 percent over the medium term. Stripping out volatile energy and food prices, inflation in January was 1.9 percent on an annual basis, Eurostat said on Wednesday.
Falling prices may help European households, but the euro zone is heading into its second recession in three years and unemployment is one of the biggest challenges for EU leaders who meet for a summit in Brussels on Thursday and Friday.
The number of people out of work in the euro zone rose to 10.7 percent in January, up from an upwardly revised 10.6 percent in December. That was far higher than the 8-percent rate when euro coins and notes began circulating in 2000, and the latest figure masks the north-south split in the euro zone's fortunes.
Unemployment in Spain rose to 23.3 percent in January, the highest level in the 17-nation currency area, but was just 4 percent in Austria.
Overall, another 185,000 people across the euro zone were out of work in January compared to December, Eurostat said.
The rise in unemployment was higher than the 10.4 percent forecast by economists in a Reuters poll. But that was perhaps not surprising, given that business managers in an EU survey released this week said they were generally pessimistic about their ability to hire new staff even as wider business confidence improves.