* Dollar on best streak of gains since May
* Euro dips below $1.18 on reports ECB eyeing exchange rate
* Chinese services growth pushes yuan higher
* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E
By Tom Westbrook
SINGAPORE, Sept 3 (Reuters) - The dollar's bounce extended on Thursday, as investors trimmed bets against the greenback and sold the euro on concerns that the European Central Bank was worried about its rise.
The bounce has lifted the greenback about 1.3% above the 28-month low it hit against a basket of currencies on Tuesday.
Few analysts expect it to hold for too long, but it gained broadly in Asia and if sustained would be the first time the dollar has climbed three sessions in a row since May.
"You could put (the dollar bounce) down to a bit of a trend reversal, it's had a long run downwards," said BNZ senior markets strategist Jason Wong.
"But if it is a floor, it's only a short-term one...everyone's pretty bearish dollars for good reason," he said, pointing to the Federal Reserve's policy outlook that will likely keep rates very low for a long time.
For about a fortnight now the dollar has been fighting to hold the line after dropping 10% from a March peak. As traders start to temper stretched bets on the euro it could post its best week on the common currency in four months.
The euro EUR=EBS fell about 0.4% to a one-week low of $1.1797 in Asia after the Financial Times reported that several members of the ECB's governing council were concerned that the euro's rise could weigh on European growth.
That followed remarks on Tuesday from ECB's chief economist Philip Lane, who said the exchange "does matter" for monetary policy, which had begun the euro's descent from above $1.20.
A speech from ECB board member Isabel Schnabel at 1500 GMT will be closely watched for any comments on the currency.
"For now, do not rule out further extension towards $1.18, but we are cautious of calling for further downside from that level," said OCBC Bank currency strategist.
It hit a three-month trough of 88.67 pence EURGBP= .
YUAN FIRM
The outlier was the yuan CNY= , which rose as far as 6.8250 per dollar in the onshore market in the wake of a survey showing a sustained recovery in China's services sector, which grew for a fourth straight month. Chinese currency pared those gains in the afternoon, to hold steady against an otherwise rising dollar, but it has put on an eye-catching 4.3% gain over the past three months.
That has investors beginning to think China's policymakers are becoming more tolerant of a stronger currency as part of a broader shift away from export-driven growth.
"Chinese leaders will be less tempted to use yuan depreciation to stimulate growth as the export sector plays a secondary role," said Mizuho's chief Asian FX strategist Ken Cheung.
Elsewhere, the Japanese yen is gradually drifting back to where it was before Shinzo Abe resigned as Prime Minister as his close ally Yoshihide Suga firms as the favourite to succeed him.
Suga formally declared his candidacy for the Liberal Democratic Party leadership on Wednesday and is expected to persist aggressive fiscal and monetary stimulus. yen slipped marginally to 106.33 per dollar. The Australian dollar AUD=D3 slipped 0.4% to $0.7307 and the kiwi NZD=D3 was down 0.3% at $0.6759.
Ahead on Thursday are purchasing managers index figures in Britain, Europe and the United States and markets are also awaiting U.S. jobs data at 1230 GMT.
U.S. payrolls figures are due Friday, with soft private jobs data on Wednesday pointing to possible disappointment of economists' expectations for 14 million new hires in August.
(Editing by Sam Holmes and Jacqueline Wong)