* Dollar index hovers near previous day's 11-month peak

* U.S. services industry activity at 8-1/2-year high in July

* Kiwi dented by fall in dairy prices, mixed NZ jobs data

* Euro stuck near nine-month lows (Updates prices, adds comments)

By Ian Chua and Masayuki Kitano

SYDNEY/SINGAPORE, Aug 6 (Reuters) - The dollar held near an 11-month high against a basket of major currencies on Wednesday, supported by upbeat U.S. data, while the New Zealand dollar took a hit from a fall in dairy prices.

The dollar index was last at 81.550, not far from Tuesday's peak of 81.626. The euro eased 0.1 percent to $1.3368 , having plumbed a nine-month trough of $1.3358 on Tuesday.

Helping to support the dollar, data on Tuesday showed U.S. services sector activity hit an 8-1/2 year high last month and factory orders surged in June, bolstering expectations of solid economic growth in the third quarter.

"We're back into the medium-term trend, which is for a higher dollar," said Jesper Bargmann, head of trading for Nordea Bank in Singapore.

Over time the euro is likely to head lower versus the dollar, due to a divergence in the outlook for monetary policies of the United States and the euro zone, he said.

Bargmann said that while the market was already short the euro, he expects these bearish bets could grow further.

In addition to the European Central Bank's policy meeting on Thursday, the focus will be on forthcoming U.S. economic data and whether they come in strong enough to push forward market expectations for the timing of a Fed rate hike, he added.

European data had been mixed on Tuesday. Euro zone retail sales rose at their fastest rate in seven years in June and business activity expanded at the second-fastest pace in three years in July.

Yet the robust growth could not mask the deflationary pressures weighing on the region, a clear worry for the ECB.

But having unveiled a raft of measures in June to spur growth, the ECB is not expected to tinker with policy this month.

The dollar held steady versus the yen at 102.56. The dollar had risen to as high as 102.93 yen on Tuesday but later backed off, with the safe haven yen finding support as equities retreated amid concerns over escalating tensions in Ukraine.

The standout currency in Wednesday's Asian trade was the New Zealand dollar, which skidded to a two-month low after milk prices fell again at an auction held by Fonterra Co-operative Group, the world's biggest dairy exporter.

It extended its decline on data showing a moderation in jobs growth at home, an outcome that some suspect could buy the central bank more time to stay on the sidelines following four successive interest rate hikes this year.