* German exports up 1.9 pct, imports up 2.3 pct
* Industry output up 1.8 pct vs f'cast unch m/m
* Bundesbank cuts 2013 economic growth forecast
* Data points to some trade rebalancing in euro zone
By Michelle Martin and Sarah Marsh
BERLIN, June 7 (Reuters) - German industrial output and trade activity rose sharply in April but the Bundesbank cut its growth forecast for this year, saying Europe's largest economy would slow down again after a second-quarter surge.
The jump in activity offered some encouragement to other euro zone states, which are counting on increased German demand to help them export their way out of the region's crisis.
But Germany's central bank said the economy would slow considerably after a strong second quarter, cutting its 2013 growth forecast by 0.1 percentage points to 0.3 percent and its estimate for 2014 growth to 1.5 percent from 1.9 percent.
The Bundesbank's 2013 prediction brought it into line with the International Monetary Fund, which halved its forecast for Germany on Monday.
However, the estimates differed in tone from those of the European Central Bank, which on Thursday stuck to its view of a gradual euro zone recovery beginning later this year and raised growth forecasts for next year.
The Bundesbank said its less optimistic stance was "due mainly to downward revisions with regard to the external environment", adding it could now see exports falling by 0.8 percent from last year.
Economists said the trade and output data raised the chances the economy would grow at a faster pace in the second quarter, after expanding just 0.1 percent in the first three months, barely avoiding a recession.
Industry output unexpectedly jumped 1.8 percent in April, while exports rose 1.9 percent and imports gained even more by 2.3 percent, official figures showed.
"But there are several reasons for caution," said Jennifer McKeown at Capital Economics. "Both the manufacturing PMI survey and industrial new orders data point to stagnation or renewed falls in industrial output ahead."
The strong April output data is partly due to a catch-up effect after construction activity in particular was hit by a harsh winter. Construction output jumped 6.7 percent in April, Economy Ministry data showed on Friday.
Holger Schmieding from Berenberg Bank forecast construction would contribute 0.3 percentage points to growth of 0.8 percent in the second quarter, noting that manufacturing output was also strong in April.
Meanwhile, figures from the Statistics Office showed imports from the euro zone rising a healthy 5.4 percent on the year in April. This helped Germany level its trade balance with the currency bloc, a sign of the re-balancing many say is needed to help the region's worst off states escape from deep downturns.
But the overall German picture on imports was still very weak due to a lack of investment, McKeown said, so "any hopes that Germany is about to provide a massive boost to peripheral (euro zone) countries are far too optimistic."
Germany's traditionally export-driven economy is relying on domestic demand to prop up growth as foreign trade looks likely to act a drag this year, given that much of the euro zone, where it sends 40 percent of its exports, is lingering in recession.
Private consumption, supported by wage hikes, moderate inflation and low unemployment, was the driving force behind German growth in the first quarter.
Imports from the euro zone may have risen in April but they fell 0.7 percent in the first four months of the year, outpaced by a 2.0 percent drop in German exports to the currency bloc.
The Bundesbank warned on Friday that German exporters' sales markets would only expand by 1.25 percent this year, which it said was considerably lower than global trade growth.
German firms are looking to China and other non-European countries as alternative markets to boost their sales. Unadjusted trade data showed exports to countries outside Europe rose by 13.6 percent on the year in April, while exports to the euro zone were up by 4.3 percent.
Tyre and car parts maker Continental AG has said improving markets in North America should help lift first-half sales to year-ago levels and chemicals firm BASF plans a hiring spree in the Asia Pacific region as it aims to double sales to customers there by 2020.