SYDNEY (Reuters) - Australian consumer sentiment rebounded modestly in June as the promise of imminent tax cuts lightened the mood, a survey showed on Tuesday, though the risk of yet higher borrowing costs loomed in the background.

The Westpac-Melbourne Institute index of consumer sentiment rose 1.7% in June from May, when it dipped 0.3%. The index reading of 83.6 showed pessimists still outnumbered optimists, much as it has for months now.

News of more cost-of-living aid from state governments likely helped sentiment ahead of a major cut to income taxes due from July 1.

However, the survey also bracketed a meeting of the Reserve Bank of Australia (RBA) which warned there were upside risks to inflation and another rise in interest rates could not be ruled out.

The survey found a sharp decline in sentiment to 80.1 after the RBA's decision, from 90.0 before the announcement. The proportion of respondents expecting higher mortgage rates in the next 12 months also rose to 48.3%, from 43.5% in May.

"The survey detail suggests positives from fiscal support measures are being negated by increased concerns about inflation and the outlook for interest rates," said Westpac senior economist Matthew Hassan.

The budget relief did see a bounce in the survey's measures of family finances, though the outlook for the economy remained deeply pessimistic.

The index measuring whether it was a good time to buy major household items firmed 4.2%, but at 79.7 remains far below its long-run average of 124.

(Reporting by Wayne Cole; Editing by Stephen Coates)