SYDNEY (Reuters) - Australia's business conditions eased sharply in May, dented by slower gains in sales and employment, suggesting demand growth is moderating in the wake of the central bank's most aggressive tightening campaign in its modern history.

The survey from National Australia Bank (OTC:NABZY) Ltd (NAB) released on Tuesday showed its index of business conditions fell by a sizeable seven points to +8 in May, but they remained just above the long-run average.

The volatile measure of confidence dipped back to negative territory, falling to -4 from April's 0, showing that the number of firms that are pessimistic outnumbered those that are optimistic.

The survey's measure of sales declined 8 points to +14 in May, the employment index fell 7 points to +4, and forward orders, a leading indictor of demand, fell to -5 in May.

"With the easing in business conditions accelerating and forward orders falling sharply, there is a growing risk that the RBA’s attempts to maintain an even keel 'run aground'," said NAB chief economist Alan Oster.

"The trend over coming months will be important as the RBA tries to assess whether it has done enough and if underlying inflation pressures are easing in a timely way."

In a worrying sign for the Reserve Bank of Australia, the survey pointed to persisting price pressures, with the measure of labour costs picking up to a quarterly rate of 2.2%, from 1.9% the previous month, and purchase costs accelerating to 2.5% from 2.2%.

The RBA surprised markets last week by raising the cash rate another quarter-point, bringing the total hikes to a whopping 400 basis points since May last year, and warned more rate hikes may be required to bring inflation to heel.

Markets have moved to price in the risk of two more hikes to 4.6%, while seeing rates staying there for the remainder of the year.