* Baosteel lowers prices for the first time in 2012
* Iron ore firmer, but upside seen limited
SINGAPORE, June 12 (Reuters) - Shanghai steel futures slipped on Tuesday, weighed down by concerns demand in top steel consumer China will remain weak through next month, prompting major producer Baosteel to cut prices for the first time this year.
Baosteel Group, the world's third biggest steelmaker and parent of Shanghai-listed listed Baoshan Iron and Steel , said it will cut prices of its main products by around 4 percent in July.
Baosteel's pricing moves are seen as a bellwether for the industry, and the last time it reduced prices was in December 2011, when Beijing's monetary tightening moves dented steel demand.
The most traded rebar contract for October delivery on the Shanghai Futures Exchange dropped 0.6 percent to close at 4,100 yuan ($640) a tonne, falling for a second time in three sessions.
The price cut sent Baosteel's share price falling more than 3 percent, although analysts and traders say it was hardly surprising.
"It was expected because China is already in a slowdown. The only concern now is whether demand will be slower than they have expected," said an iron ore trader in Hong Kong.
Despite soft demand, China's legion of steel mills continued to boost output, hoping to protect their market share in a highly fragmented industry. That has supported prices of key raw material iron ore as mills try to keep enough inventories.
The country, which produces around half of the world's steel, made 61.234 million tonnes of crude steel in May, up 2.5 percent from a year ago and more than April's 60.575 million tonnes, government data showed on Monday.
"We are seeing increasingly firm interest from buyers for replenishing purposes," said the Hong Kong trader, referring to iron ore.
"There are almost no traders out there taking positions now because they feel the price upside moving forward is extremely limited. However, downside is limited as well."
Miner BHP Billiton sold 58-percent grade Yandi iron ore fines at $124 a tonne, including freight cost, on Monday, the same level as late last week and a price "which a lot of buyers are willing to buy," he said.
Benchmark iron ore with 62 percent iron content .IO62-CNI=SI gained 0.7 percent to $132.30 a tonne on Monday, according to Steel Index, rising for a second straight day.
Indian iron ore exporter Sesa Goa is selling 70,000-80,000 tonnes of 54-percent grade iron ore lumps at a tender on Tuesday, said a Singapore-based trader.
Sesa Goa is also selling the same volume of 56-percent grade lumps at the same tender, he said.
Shanghai rebar futures and iron ore indexes at 0706 GMT
Contract Last Change Pct Change
SHFE REBAR OCT2 4100 -23.00 -0.56
PLATTS 62 PCT INDEX 134.25 +0.25 +0.19
THE STEEL INDEX 62 PCT INDEX 132.3 +0.90 +0.68
METAL BULLETIN INDEX 134.3 +0.42 +0.31
Rebar in yuan/tonne
Index in dollars/tonne, show close for the previous trading day
($1 = 6.3694 Chinese yuan)