By Wayne Cole

SYDNEY, May 25 (Reuters) - The Australian and New Zealand dollars rallied on Monday as investors wagered a deal in the U.S.-Iran war was getting closer, albeit in fits and starts, sending oil prices lower and boosting risk appetite.

The Aussie climbed 0.5% to $0.7165 AUD=D3, but stopped short of resistance around $0.7184. The major bull target is up at the recent four-year peak of $0.7272, with support at $0.7080.

The kiwi dollar also added 0.5% to $0.5875 NZD=D3, testing resistance at $0.5887. A break higher would target $0.5991, while support is down at $0.58165.

Hopes for progress in re-opening the Strait of Hormuz helped the Aussie recover from a setback last week when a soft set of jobs data was taken as lessening the chance of a near-term hike in interest rates.

Markets now imply just a 12% probability of a quarter-point rise in the 4.35% cash rate at the Reserve Bank of Australia's next meeting on June 16. That rises to around 50% for August, and 80% by September. 0#AUDIRPR

The dovish shift pulled 10-year bond yields AU10YT=RR down 15 basis points last week to stand at 4.891%, significantly outperforming U.S. debt. That narrowed the premium over Treasuries to 33 basis points, less than half the spread seen just a month ago.

The Reserve Bank of New Zealand meets on Wednesday with markets implying an 80% chance rates will stay at 2.25% and only one of 29 analysts polled tipping a hike. 0#NZDIRPR

Swaps imply around an 80% chance of a rate rise in July and 2.50% is fully priced for September, with rates seen reaching 3.5% over the next year or so.

The RBNZ is almost certain to lift its own projection for inflation and for the official cash rate which had been at 2.4% for December and just 2.8% by the end of 2027.

"We suspect that the December 2026 quarter projection will lift by around 40-50bp to around 2.8%," said Kelly Eckhold, chief NZ economist at Westpac. "This would signal two 25bp rises and a chance of a further increase through the balance of 2026."

"We also expect a live debate this week on the option to raise the OCR to 2.5%, with the decision likely going to a vote."

At the last meeting, the board discussed whether a pre-emptive tightening might be needed to anchor inflation expectations given the rising cost of energy and food.