* Weak U.S. economic data sinks dollar
* U.S. service sector growth slows to weakest since 2010
* Dollar falls more than 1 percent vs yen
* Australian dollar rises 1.3 percent as RBA keeps rates unchanged
* New Zealand dollar up 1.4 percent after strong dairy auction (New throughout, updates prices and market activity to U.S. market open)
By Dion Rabouin
NEW YORK, Sept 6 (Reuters) - The dollar tumbled on Tuesday after economic data showed the U.S. service sector grew at its slowest pace since early 2010, which dimmed expectations for a near-term interest rate increase from the Federal Reserve.
The dollar fell to a one-week low against the Japanese yen after the data, and the British pound rose to its highest level against the dollar since mid-July.
The Institute for Supply Management's non-manufacturing purchasing managers' index fell to 51.4 last month, far short of economists' expectations and the largest one-month drop since November 2008. you pair that with data we got Friday, which was non-farm payrolls, disappointing some, what it does is it starts to kick back interest rate expectations past the September meeting and even lowering them in December too," said John Doyle, director of markets at Tempus Inc in Washington.
"You're seeing slightly softer data over the last couple of trading sessions equals less likelihood the Fed will raise rates at the meeting this month and with that comes a slightly weaker dollar."
The service sector makes up more than two-thirds of the U.S. economy.
Friday's U.S. non-farm payrolls report showed employers in the United States added 151,000 jobs last month, missing economists' expectations and falling well below readings in June and July, which both showed more than 250,000 jobs added in each month.
On Tuesday, the dollar fell more than 1 percent against the yen JPY= , slipping to 102.05 yen per dollar.
The British pound GBP= rose by 1 percent against the dollar, touching a fresh seven-week high at $1.3443. The euro EUR= rose to $1.1255, its highest since Aug. 26 after the data.
The dollar index .DXY dropped 1 percent to 94.821, its lowest since Aug. 26.
The New Zealand dollar was the biggest gainer among major currencies, rising 1.4 percent against its U.S. counterpart to its highest level since May 2015. The kiwi was boosted by the weak U.S. data and a rise in milk prices after a strong dairy auction in New Zealand. Australian dollar AUD= jumped 1.3 percent against the greenback after the data. The Aussie was also bolstered by the Reserve Bank of Australia's decision to leave interest rates unchanged at 1.5 percent and minimal commentary from the central bank on the currency's 10 percent rise against the U.S. dollar since January.