SYDNEY, July 4 (Reuters) - The Australian dollar stood tall near a six-month high on Thursday, after cracking major resistance levels overnight as soft U.S. economic data fanned hopes of a September rate cut, supporting bonds.

The Aussie also made further gains on its New Zealand cousin and scaled a fresh 33-year peak versus the battered yen due to robust demand from carry trades - where traders borrow a currency with low interest rates to invest in a currency with higher yields.

The Australian dollar firmed 0.2% to $0.6718, having gained 0.6% overnight to as far as $0.6733, its highest level in six months. The currency also snapped the top-end of the recent trading range of $0.6714, helped by market wagers that the next move in local rates could be higher.

The kiwi dollar got a respite from recent selling pressures. It edged 0.1% higher to $0.6108, having climbed 0.4% overnight to as far as $0.6129, and bounced off its 200-day moving average at $0.6071.

Both currencies rallied after overnight data showed U.S. services sector contracted last month, with employment notably weak ahead of the June payrolls report due on Friday. Economists forecast an increase of 190,000 jobs in June after a jump of 272,000 in May.

"It (AUD) needs to see a sustained break above resistance at 0.6710/20, a development that it is closer to achieving and likely hinges on the outcome of tomorrow night's non-farm payrolls data," said Tony Sycamore, an analyst at IG.

Markets lifted the probability of a September rate cut from the U.S. Federal Reserve to 76%, from 65%. Back in Australia, investors pared back the risk of an interest rate hike in August to 20% from about 30% a day ago.

Still, the risk of further tightening in Australia contrasted with bets that rates in New Zealand will be lower this year. The Aussie climbed for seven consecutive sessions to NZ$1.0989, just below a seven-week top of $1.0998 hit on Wednesday.

Australian bonds rallied in tandem with U.S. Treasuries, but soon lost steam and ran into some selling pressures. Ten-year government bond futures gained as much as 8 ticks before settling at 95.585, up 2 ticks for the day.

The Aussie was fetching 108.37 yen, having hit a fresh 33-year high of 108.5 yen overnight, and the kiwi was trading at 98.58 yen, hovering near a 38-year top of 98.76 yen. (Reporting by Stella Qiu; Editing by Sherry Jacob-Phillips)