* Euro rises as German industry orders jump
* Investors wary of pushing euro lower before ECB meets
* U.S. Fed's Williams urges caution on trimming stimulus
LONDON, Nov 6 (Reuters) - The euro rose on Wednesday after stronger-than-expected German industry orders increased uncertainty over whether the European Central Bank would cut interest rates this week in response to a steep fall in inflation.
The euro has dropped sharply from levels above $1.38 touched before last week's inflation data. But some investors were wary the ECB may not adopt a very dovish tone at Thursday's policy meeting and took profit on the currency's fall, traders said.
Some see a risk that the central bank could lower interest rates or at least lay the ground for such a move, though only one of 23 money market traders polled by Reuters expects a cut on Thursday.
The single currency extended gains after data showed German factory orders jumped by 3.3 percent during September, well above the 0.5 percent economists had expected.
The euro was up 0.3 percent at $1.3515, well above Monday's low of $1.3442 and trendline chart support at $1.3454.
"The euro has come off quite a long way on the potential that there could be a rate cut. We have a day to go and no one is certain that the ECB will cut rates," said Jane Foley, senior currency strategist at Rabobank.
"Now we have had stronger German data and the market doesn't want to oversell the euro because it is not confident that (ECB President Mario) Draghi will have any cards to play."
Euro zone private sector surveys showed October activity growth slowed less than previously estimated.
The euro was also helped by comments from U.S. Federal Reserve official John Williams, which weighed on the dollar. He said the Fed should wait for stronger evidence of growth momentum before trimming bond-buying.
But a report on Tuesday showing U.S. service-sector activity picked up in October suggested the economy may not have suffered badly from the partial government shutdown. This kept alive the prospect of the Fed scaling back stimulus in the coming months.
Carl Hammer, chief currency strategist at SEB in Stockholm, said he expected euro/dollar movements to be limited to within 1-2 cents either side of $1.35.
"An ECB rate cut would be negative for the euro because it would play into the hands of short-term speculators as the market is quite long of euros, but it would not really alter the long-term picture." He said a rate cut would have limited effect because rates were already near zero
The dollar index, which measures the greenback's value against a basket of currencies, slipped 0.2 percent to 80.545 , down from a seven-week high of 80.930 set on Monday.
Sterling earlier hit a one-week high against the dollar and a one-month peak against the euro after stronger-than-expected industrial output data.