* Euro initially weakens after German ZEW sentiment data but steadies
* Dollar index hovers near five-week high
* U.S. import prices fall on cost of oil
* Yen selling curbed by sharp rise in Japan bond yields
By Julie Haviv
NEW YORK, May 14 (Reuters) - The euro was steady on Tuesday as stronger-than-expected euro zone industrial output offset data showing German investor morale pointing to a tepid recovery in Europe's largest economy.
While the euro, down roughly 1.4 percent against the dollar in May, found support earlier in the session from signs of a robust response to a Spanish debt sale, investors remain cautious given the region remains mired in a recession.
Also weighing on the euro is the risk that the European Central Bank could slash its deposit rate, at which banks park surplus funds with it, to negative. Depositors would be charged for leaving funds at the ECB, which would pressure the euro.
Germany's ZEW think tank said its monthly poll of economic sentiment rose to 36.4 points from 36.3 in April, falling short of expectations for a reading of 38.3.
Other data, however, showed output at euro zone factories rose much more strongly than expected in March, but the overall picture remained mixed as industrial output decreased in France and Italy, the bloc's second and third largest economies.
"The euro seesawed after the mixed data from the region largely offset (each other), keeping in place sentiment that's largely bearish," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington D.C..
"Expectations that the ECB might further cheapen borrowing rates to spur recovery at a time when the days of the Fed's super-easy monetary policies appear increasingly numbered have been among the chief catalysts driving the euro lower," he said.
The euro last traded flat against the dollar at $1.2978 after falling for three straight sessions. That is above the session trough of $1.2946, but well below the session high of $1.3028. The euro on Friday hit a five-week low of $1.2935.
Against the yen, the euro was down 0.1 percent at 131.90 yen .
Growth will return to the euro zone's recession-mired economy in the second half of this year, but economists see no chance it will recover strongly until at least 2015, a Reuters poll showed on Tuesday. For other stories from the poll, see:
While some ECB policymakers have talked openly of cutting the deposit rate below its current level of zero percent, a majority of economists and traders polled in the past week think such a move is unlikely.
YEN GAINS AFTER SHARP DROP
The dollar dropped against the yen for the first time in four sessions, as investors paused from the recent swift and sharp rally that ignited last Thursday when it hit the key 100 yen mark.
The dollar last traded at 101.74, down 0.1 percent on the day, but not far from a 4 1/2-year high of 102.14 yen set on Monday.
Traders said the recent yen-selling spree has paused due to a spike in Japanese government bond yields, which reduces the relative attraction of foreign bonds for Japanese investors.
The Bank of Japan could ease monetary policy as early as October if prices don't rise as quickly as projected, according to economists polled by Reuters, who also upgraded their growth forecasts.
But the dollar was underpinned by Monday's data showing U.S. retail sales unexpectedly rose in April, and could gain further if upcoming U.S. economic data pointed to a recovery.
U.S. import prices fell in April due to a drop in oil costs, a positive sign for household finances that also pointed to benign inflation pressures.
More U.S. data will emerge this week including Wednesday's industrial production, housing starts and consumer prices on Thursday and consumer sentiment data on Friday.