Australia shares retreat as key 6,000 mark remains out of reach

* Benchmark spurns 6,000-point level

* Iron ore rebound fails to lift resources

* Health stocks dragged by Wall Street (Adds analysis, quotes, stocks on the move)

SYDNEY/WELLINGTON, April 28 (Reuters) - Australian shares fell on Tuesday, the benchmark retreating from the key psychological barrier of 6,000 points, as investors shrugged off a rebound in iron ore prices and cashed in their profits after a recent winning streak.

Iron ore futures have risen in recent sessions as Chinese steel mills pick up their purchasing of the raw building material, but investors still avoided resource stocks amid concerns the pick-up may be short-lived.

A weaker finish on Wall Street also dragged down Australian health stocks after that sector led U.S. equities lower.

By 0235 GMT, the S&P/ASX 200 index was down 15.2 points or 0.3 percent at 5,967.0, having risen for the past three sessions and having reached a 7-year-closing high of 5,982.7 on Monday.

"That 6,000 level is becoming more and more significant," said CMC Markets chief market strategist Michael McCarthy.

"Each time we pull back from that level it becomes a more significant hurdle so it looks like it will need a fairly significant change for the market to get through that."

Echoing Wall Street, health stocks were the biggest drag in Australia with global blood plasma products maker CSL down 1.5 percent, medical device maker ResMed (NYSE: RMD - news) and hearing aid maker Cochlear (Other OTC: CHEOY - news) both off by 3 percent.

Mining giant Rio Tinto (Xetra: 855018 - news) fell 1 percent while rival BHP Billiton (NYSE: BBL - news) held steady. Energy stocks tracked the commodity's spot price lower, with Oil Search down 2 percent and Woodside Petroleum (Xetra: WOPA.DE - news) down 0.2 percent.

Banks were mixed, with Westpac Banking Corp and Australia and New Zealand Banking Group both fell about half of 1 percent, while National Australia Bank and Commonwealth Bank of Australia (Other OTC: CBAUF - news) rose 0.2 percent each.

Elsewhere, recruiting agent Ashley Services Group dropped by two thirds after issuing an earnings downgrade.

New Zealand's benchmark NZX50 index rose 20.6 points or 0.4 percent to 5,785.99 as gains in the construction, retail and services sectors lifted the index.

Construction materials maker Fletcher Building (NZSE: FBU.NZ - news) rose nearly 2 percent after a fund manager said it reduced its stake in the firm, the largest on the NZX50.

Steel and Tube rose 1.8 percent while casino operator SkyCity Entertainment rose 1.8 percent and online auction site Trade Me (NZSE: TME.NZ - news) pushed up 1.4 percent.

Orion Health Group rose 3 percent after saying full-year operating revenue rose 7 percent.

For more individual stocks activity click on (Reporting by Byron Kaye and Naomi Tajitsu; Editing by Jacqueline Wong)