SYDNEY, May 29 (Reuters) - The Australian dollar got a brief lift on Wednesday after a reading on local inflation surprised on the high side, slugging bonds and adding to risks interest rates may yet have to rise further.

Data showed the monthly consumer price index rose 0.7% in April, from March, when analysts had looked for an increase of around 0.5%. Higher prices for health insurance, clothing, petrol and holidays all contributed to the increase.

The annual pace picked up to a five-month high of 3.6%, while core inflation accelerated to 4.1% and further away from the Reserve Bank of Australia's (RBA) target band of 2-3%.

The RBA had anticipated a pick up in headline CPI this quarter, but thought the core would slow to an annual 3.8%.

"The key implication overall is that some inflation components are looking sticky, while goods is not helping further on disinflation," said Tapas Strickland, head of market economics at NAB.

"If the labour market or broader capacity pressures do not loosen as much as we expect and inflation proves more persistent, we think the RBA's preferred response would be holding for longer."

Markets responded by nudging up the probability of a rate rise to 20%, though the RBA itself has made it clear the bar to a hike is a high one.

Futures also pushed out the likely timing of a first rate cut to July or August next year.

Three-year bond futures were down a sharp 12 ticks at 95.930, though much of that was in response to an overnight increase in U.S. Treasury yields.

The Aussie firmed a fraction to $0.6652, having got as far as $0.6680 overnight before running out of steam. Support comes in around $0.6640 and $0.6592, with resistance at the May top of $0.6714.

The kiwi dollar held at $0.6136, after hitting a 10-week high of $0.6170 the previous session. Support lies at $0.6135 and $0.6084.

Over in New Zealand, an ANZ survey showed business confidence slipped in May, while pricing intentions eased and inflation expectations dipped to 3.6% from 3.8%.

"Also encouraging for the Reserve Bank, there was finally a fresh low in the net proportion of firms intending to raise their prices in the next three months," said ANZ chief economist Sharon Zollner.

"We're optimistic that they'll be able to cut earlier than they expect as slowing domestic demand continues to weigh on CPI inflation pressures." (Reporting by Wayne Cole Editing by Shri Navaratnam)