* Dollar sat near one-week lows on yen and euro
* Swiss franc, yen, gold rise as investors flock to safety
* Pound rangebound as EU mulls Brexit offer
By Tom Westbrook
SINGAPORE, Oct 3 (Reuters) - The dollar nursed losses on Thursday, hitting near one-week lows against the euro and yen, amid signs of a slowdown in U.S. economic growth and a deepening of global trade tensions.
The greenback fell overnight after data showed hiring by U.S. private employers had slowed in September, the latest indicator that the Sino-U.S. trade dispute is hurting the world's largest economy. weaker-than-expected numbers follow a separate release on Tuesday that showed a sharp decline in factory activity that sent stock markets and bond yields tumbling.
"The trend certainly in U.S. data had been consistently beating expectations, so the sudden reversal of fortunes has created a rapid re-assessment," said Chris Weston, head of research at brokerage Pepperstone Group in Melbourne. "There is not a lot of good news to inspire the bulls."
In Asian hours, investors headed for safety. Stocks fell. Gold XAU= and the Swiss franc CHF= inched higher.
The dollar weakened slightly to 107.13 Japanese yen JPY= and $1.0962 per euro EBS= , both only a fraction above a one-week lows touched overnight.
It held close to a one-week low against the New Zealand dollar NZD=D3 at $0.6264 per kiwi and weakened a little against the beaten-up Australian dollar AUD=D3 to $0.6714.
The weakness in the U.S. follows a slew of poor economic data from Europe and signs of a hastening slowdown in China.
Adding to concerns, the United States won approval on Wednesday to levy tariffs on $7.5 billion worth of European goods over illegal subsidies handed to Airbus, threatening to trigger a transatlantic trade war.
The next readings on global economic health will be European August retail sales and a German service sector survey due on Thursday, and September's U.S. non-manufacturing ISM survey due at 1400 GMT.
Against a basket of currencies .DXY the dollar was flat at 99.022.
The pound GBP=D3 was steady at $1.2302 after fluctuating in a tight range as British Prime Minister Boris Johnson proposed an all-island regulatory zone in Ireland in his final pitch for a Brexit deal before the end of the month. outlook, however, remained uncertain after a cool response to the proposal from Brussels, leaving a no-deal exit from the European Union on Oct. 31 a real possibility.
"The question appears to be whether there is enough middle ground for the two sides to come to some sort of agreement by the time of the EU Summit on Oct. 17," said Rodrigo Catril, senior FX strategist at National Australia Bank in Sydney.
In offshore trade, the Chinese yuan CNH= was steady at 7.1452 per dollar, with trade subdued as Chinese markets are closed until Monday for public holidays.