SYDNEY, May 30 (Reuters) - The Australian and New Zealand dollars steadied on Thursday after suffering a setback from a surge in U.S. bond yields which soured risk appetites, while clouding the outlook for rate cuts globally.

The Aussie was pinned at $0.6605, having pulled back from $0.6667 overnight as the U.S. dollar rose across the board. Immediate support comes in at $0.6592, with resistance at$0.6680.

The kiwi dollar eased a fraction to $0.6108, after falling 0.4% the previous session. Resistance lies at the $0.6170 top hit at the start of the week, with support around $0.6084.

Bonds had another rough session as Treasury yields rose to one-month highs, lifting Australian 10-year yields to a three-week peak of 4.476%. Three-year bond futures were down 13 ticks for the week so far at 95.890.

Markets were still smarting from a surprisingly high reading of Australian inflation for April, which added to the risk that the Reserve Bank of Australia (RBA) might have to hike rates again.

Futures now imply a 27% chance of a rise in the 4.35% cash rate, up from 14% before the data.

"The slow disinflation process in Australia has been evident for some time," said Paul Bloxham, head of Australian economics at HSBC. "Despite the slowdown in growth, the supply-side of the economy has been constrained, and productivity has been weak."

"Our central case is that the RBA's cash rate will be on hold through 2024 with rate cuts not beginning until Q2 2025."

Data out on Thursday showed business investment beat forecasts with a rise of 1.0% in the first quarter, thanks to a 3.3% jump in spending on plant and machinery.

That strength will help balance unexpected weakness in construction work during the quarter, though economic growth is still likely to be paltry at best.

In New Zealand, the government released a budget that predicted a wider deficit amid sluggish economic growth and rising unemployment.

The government said tax relief measures would be offset by savings and new revenue, meaning the measures were expected to be broadly neutral for inflation.

The government now plan to issue NZ$38 billion of bonds in 2024/25, up a modest NZ$2 billion on the previous outlook. (Reporting by Wayne Cole; Editing by Michael Perry)