* Benchmark iron ore eyeing longest winning streak since Nov
* China daily steel output near record highs
By Manolo Serapio Jr
SINGAPORE, June 20 (Reuters) - Spot iron ore prices mostly edged higher on Wednesday, putting the benchmark rate on course for a ninth consecutive day of gains - its longest rally in seven months - as traders took cargoes betting Chinese buyers would follow suit.
China's daily crude steel output neared record highs in early June, based on the latest industry estimate, suggesting producers may continue to replenish iron ore stockpiles, although some traders say prices may soon peak.
Price offers in top iron ore importer China for cargoes from major producer Brazil rose by $2 a tonne on Wednesday, while prices for material from other origins were mostly steady, according to industry consultancy Umetal.
That could further lift the benchmark 62-percent grade iron ore .IO62-CNI=SI which marked its eighth straight day of gains on Tuesday, its longest run since mid-November when the price of steel's raw material rose for 14 days in a row.
Iron ore rose 0.4 percent to $136.60 a tonne, according to price provider the Steel Index, the highest since May 14.
"The market looks fairly well supported at the moment. There's a fair number of transactions going through," an iron ore trader in Singapore said.
Top miner Vale is offering 170,000 tonnes of 65-percent grade Brazilian Carajas iron ore fines at a tender on Wednesday, while third-ranked BHP Billiton will sell 70,000 tonnes of 62.7-percent grade Australian Newman fines.
The current run-up in iron ore began after a fall in prices to two-week lows drew Chinese steel mills back into the market to restock. That prompted traders to snap up cargoes and take positions on hopes the restocking will continue with most mills running at full capacity.
China's daily crude steel output rose 2 percent to 1.999 million tonnes in the first 10 days of June from the previous 10-day period, as large mills ramped up output, according to the China Iron and Steel Association.
The run-rate is close to the record 2.045 million tonnes posted in early May, and suggests producers are anticipating demand to recover as China acts to boost its economy.
"The production increase is disappointing to us given the increased number of reports of 'accelerated maintenance outages'taking place, but not entirely surprising, as we have been concerned that Beijing's interest rate cut could end up backfiring causing steelmakers to ramp up production in anticipation of future demand," Chicago-based Steel Market Intelligence said in a note.
Still, the iron ore rally could soon run out of steam.
"We're seeing a bit of pullback in bids because market seems to have peaked," said an iron ore trader in Hong Kong.
An Australian miner sold five iron ore shipments on Tuesday, with three cargoes sold at prices that were slightly lower than previous deals, the Steel Index said.
Shanghai rebar futures and iron ore indexes at 0519 GMT
Contract Last Change Pct Change
SHFE REBAR OCT2 4147 +21.00 +0.51
PLATTS 62 PCT INDEX 138.5 +0.50 +0.36
THE STEEL INDEX 62 PCT INDEX 136.6 +0.60 +0.44
METAL BULLETIN INDEX 136.8 +0.72 +0.53
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day