SYDNEY (Reuters) -Australia's property prices jumped in June to another record high as rate cuts and expectations of more to come boosted buyer demand in the face of low housing supply, data showed on Tuesday.

Figures from Cotality showed national home prices rose 0.6%to a new peak price of $837,586 in June, up from a gain of 0.5% the previous month, for a fifth straight month of gains following a shallow downturn between November and January.

The monthly gain was led by a jump of 0.8% in Perth, followed by Brisbane with an increase of 0.7% and Sydney, with a rise of 0.6%. Hobart was the only capital city to show a fall of 0.2%.

Falling interest rates have been a clear catalyst of the renewed momentum in housing prices, said Cotality's research director, Tim Lawless.

"The first rate cut in February was a clear turning point," he said.

"An additional cut in May, and growing certainty of more cuts later in the year, have further fuelled positive housing sentiment, pushing values higher."

Lawless said advertised supply was tracking 5.8% below the corresponding time a year ago, while auction clearance rates have risen above the decade-average in the last two weeks of June.

The Reserve Bank of Australia has cut interest rates twice to a two-year low of 3.85%. Further cooling in inflation in May has markets almost fully price in a move next Tuesday, with almost four rate cuts priced in by early next year.

That has helped consumer confidence to rebound and improved borrowing capacity, although affordability constraints and strict lending policies are likely to keep a lid on the housing exuberance.

A Reuters poll of economists found that Australia's home prices are likely rise a steady 4% to 5% a year over the next three years, on top of a jump of 40% in prices in the past five years.

"Given the upside risk that housing values will accelerate further from here as interest rates reduce, the reality is we will likely see home values rise by more than this over the coming 12 months," said Lawless.

($1=A$1.5618)

(Reporting by Stella Qiu; Editing by Clarence Fernandez)