* Shanghai rebar in 4th day of decline, hits 3-week low
* Chinese mills live hand to mouth on iron ore needs
* Australia sees 10 pct rise in iron ore exports
SINGAPORE, June 27 (Reuters) - Spot price offers for Australian and Brazilian iron ore cargoes in China dropped on Wednesday as demand thinned amid a sluggish Chinese steel market that is likely to extend through next month as rains slow construction projects.
Demand for steel in China, the world's biggest consumer and producer, has been largely weak this year, driving steel prices down nearly 3 percent as slower activity in the world's No. 2 economy curbs demand.
Demand is also seasonally weak during the summer as the hot weather slows construction activity. But now, so will the rains.
"All our clients are bearish. They think steel demand in July will be worse because it's been raining in most parts of China, so construction work could slow down," said an iron ore trader in Shanghai.
"There's no incentive to buy iron ore now."
Price offers for Australian iron ore cargoes fell by $1 per tonne on Wednesday, according to industry consultancy Umetal. Offers for Brazilian material dropped by $2 a tonne.
Australia is the world's biggest iron ore producer, followed by Brazil. Australia on Wednesday predicted a 10 percent rise in iron ore exports to 510 million tonnes in the next fiscal year as miners expand output to meet demand from top market China.
Benchmark iron ore with 62 percent iron content .IO62-CNI=SI dropped 1.2 percent to $135.40 a tonne on Tuesday, its lowest since June June 15, based on data from Steel Index.
"Mills continue to live hand to mouth, operating with as little inventory as possible and buying small volumes at port when necessary," Steel Index said.
OUT OF STEAM
It marked a second straight day of decline for iron ore as a recent rally ran out of steam. The price rose for 10 consecutive days up to last Thursday, its longest winning streak since mid-November, as traders bet that high steel output in China will push mills back into the spot market to restock.
"Most mills have already replenished in the past weeks so there's no need for them to buy now," said another trader in Shanghai.
"We have not bought anything recently and we still continue to sell our port stocks in small lots. It's not easy because the market keeps changing so we have to adjust prices several times.
But we're trying to sell more because it looks like prices will drop some more in the short term."
Prices at sale tenders by miners have been falling this week, including those sold by BHP Billiton on Monday.
Top miner Vale sold 163,000 tonnes of 64.81-percent grade iron ore at $147.05 a tonne on Tuesday via a tender, against a previous sale above $150, traders said.
Chinese mills may be prodded to curb output if steel demand remains weak in July, although some may already be cutting production.
"In China, iron ore inventories at steel mills are falling in volume terms, but since steel mills are now reducing production measured on days of consumption basis, iron ore inventories are rising and now exceed 31 days," Macquarie said in a note.
That puts any price recovery at risk unless steel demand improves and mills increase output, said Macquarie.
The most-traded steel rebar contract for October delivery on the Shanghai Futures Exchange hit a three-week low of 4,061 yuan ($640) per tonne on Wednesday, its fourth daily loss in a row. By the midday break, it was down 0.2 percent at 4,070 yuan.
Shanghai rebar futures and iron ore indexes at 0500 GMT
Contract Last Change Pct Change
SHFE REBAR OCT2 4070 -6.00 -0.15
PLATTS 62 PCT INDEX 137.5 -1.50 -1.08
THE STEEL INDEX 62 PCT INDEX 135.4 -1.70 -1.24
METAL BULLETIN INDEX 137.62 -0.15 -0.11
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day
($1 = 6.3629 Chinese yuan)