* Analysts link weaker output data to seasonal effects
* Fundamentals remain strong and output should rebound
* U.S. import tariffs biggest threat (Adds industry, minister reaction to U.S. tariffs)
BERLIN, March 9 (Reuters) - German industrial output fell unexpectedly in January for the second month in a row and exports also sank, adding to signs that Europe's largest economy began the year on a weak footing, although analysts said the outlook remains robust.
The data on Friday was seen as a reflection of seasonal factors rather than signaling a structural slowdown. Economic activity in Germany typically eases in the winter months because of extended holidays, while this year's unusually warm January led to a decline in energy output.
Industrial output fell by 0.1 percent, the Economy Ministry said, its second consecutive fall after a dip of 0.5 percent in December and confounding expectations in a Reuters poll for a 0.5 percent rise.
Separate figures from the Federal Statistics Office showed both exports and imports had fallen unexpectedly by 0.5 percent in January, undershooting a Reuters forecast for a 0.3 percent increase in exports and stagnating imports.
The seasonally adjusted trade balance was unchanged at 21.3 billion euros ($26.22 billion).
The figures come one day after industrial orders slumped by a bigger-than-expected 3.9 percent in January.
"The weak start to the new year is nothing new for the German economy," Carsten Brzeski of ING Diba said in a note.
"It is a phenomenon witnessed more often in recent years that German economic data has been overly sensitive to seasonal effects and vacation planning."
Unusually warm weather resulted in activity in the energy sector falling by 3.3 percent. Construction sank by 2.2 percent, a breakdown of the output data showed. Manufacturing output was hampered by workers' strikes.
"We expect production to rebound in February," Stephen Brown of Capital Economics wrote in a note. "After all, unseasonably cold weather will have boosted energy output and, more generally, the business surveys paint a positive picture of underlying conditions."
DIALOGUE, NO TRADE WAR
The prospects for the German economy look rosy, with capacity utilization at its highest level since 2008 and companies reporting full order books.
U.S. President Donald Trump's import tariffs are one of the main risks for Germany, which last year exported more to the United States than any other country.
"Some darker clouds have appeared in the German economic sky," said Brzeski, referring to Trump's steep tariffs. "New protectionism would definitely hurt the self-proclaimed export world champion."
The tariffs have alarmed the German government and industry groups, who have urged a commitment to free trade.
"German industry is extremely concerned about the decision of the U.S. government to impose far-reaching punitive tariffs," the DIHK Chambers of Industry and Commerce, BDA employers association, BDI industry association and German Confederation of Skilled Crafts (ZDH) said in a joint statement.
"To prevent a spiral of protectionism, Germany and the European Union must continue to stand up (for) the global world trade system."
Separately, Germany's steel association called on the EU to come up with effective countermeasures to protect the local steel industry.
"With this decision, the USA has largely sealed itself off from the rest of the world," association president Hans Juergen Kerkhoff said in a statement, adding there was a risk that steel might now flood the European market.
The EU's trade chief said the bloc expects to be excluded from the tariffs but will go to the World Trade Organization to impose its own measures if Washington presses ahead.
Economy Minister Brigitte Zypries said Trump's tariffs would be a burden for companies in Germany.
"He has ordered punitive tariffs that do not conform with WTO rules and by doing so is increasing consumer prices and making the work of our companies -- both large and small -- harder," she said in a statement.
BDI President Dieter Kempf said he did not believe the era of free trade was over after Trump's announcement of tariffs on steel and aluminum imports, and that EU should not over-react.
But "the U.S. needs to feel some pressure," he added, urging dialog to avoid an all-out trade war. ($1 = 0.8122 euros) (Additional reporting by Gernot Heller in Berlin and Christoph Steitz in Frankfurt Editing by Catherine Evans)