UPDATE 1-Iron ore steady, but headed for best week in a month

* Iron ore prices may fall further amid oversupply-CISA

* Shanghai rebar also steady, but up 2 pct on week

(Updates rebar price) By Manolo Serapio Jr

SINGAPORE, Oct 12 (Reuters) - Spot iron ore prices in top importer China steadied on Friday after a rally earlier this week spurred caution among buyers Who are worried demand in the world's top steel consumer might not rebound significantly.

But iron ore is up 11 percent so far for the week, its best showing in a month after prices surged earlier this week as Chinese steel mills replenished stockpiles after a week-long holiday.

"I think the Chinese guys that were caught short have now covered and that if there is much on tender today it will go at weaker numbers and we will end the week on a softer note," said Jamie Pearce, head of iron ore brokering at SSY Futures, part of the shipbroking group Simpson Spence and Young.

Price offers for imported iron ore cargoes in China, including those from top supplier Australia, were unchanged on Friday, traders said.

Benchmark 62-percent grade iron ore

fell 1.6 percent to $115.80 a tonne on Thursday, after hitting an 11-week high of $117.70 on Wednesday, according to data provider Steel Index.

Prices for iron ore cargoes sold by miners Vale

and BHP Billiton

have dropped over the past two days after rising in the previous two as mills became reluctant to chase prices higher, traders said.

"It will be interesting to see how it develops next week because it could be a case of whoever shows their hand first will set the tone for the market," said Pearce.

Despite recent gains in both futures and spot steel prices, analysts and traders say there hasn't been a meaningful rebound in end-user steel demand in China so far, with uncertainty hanging over a market waiting to see whether Beijing will unleash more economic stimulus and what's ahead for the country after the once in a decade leadership transition next month.

"It's very sentiment driven at the moment and we are seeing a lot of mixed sentiment," said Pearce.

The most active rebar contract for January delivery on the Shanghai Futures Exchange

closed little changed at 3,639 yuan ($580) a tonne. Rebar, used in construction, rose 2 percent for the week after hitting a two-month high of 3,699 yuan on Wednesday.

Since the middle of September, prices of steel products have only recovered slightly, with raw material cost also rising, the China Iron and Steel Association (CISA) said on its website on Thursday.

"The heavy losses facing a large number of steel enterprises are unlikely to improve in the coming period, and iron ore prices remain in a downward trend," the industry group said.

With China's steel production falling and iron ore in oversupply, CISA said there remains room for iron ore prices to decline.

China's average daily crude steel output dropped 0.7 percent to 1.843 million tonnes between Sept 21-30, compared to the preceding 10 days, CISA data showed.

For all of September, average daily steel output fell to 1.858 million tonnes from 1.894 million tonnes in August.

Shanghai rebar futures and iron ore indexes at 0703 GMT

Contract Last Change Pct Change SHFE REBAR JAN3 3639 +5.00 +0.14 PLATTS 62 PCT INDEX 118.5 -0.25 -0.21 THE STEEL INDEX 62 PCT INDEX 115.8 -1.90 -1.61 METAL BULLETIN INDEX 117.67 -1.42 -1.19 Rebar in yuan/tonne

Index in dollars/tonne, show close for the previous trading day

($1 = 6.2770 Chinese yuan)

(Additional reporting by David Stanway in BEIJING; Editing by Miral Fahmy)

((manolo.serapio@thomsonreuters.com)(+65 6870 3884)(Reuters Messaging: manolo.serapio.reuters.com@reuters.net))