* Overall steel demand remains tepid
* Mills buy more higher-grade iron ore, lifting prices (Updates closing prices)
SHANGHAI, Jan 2 (Reuters) - Chinese steel futures rose on the first trading day of the new year, but concerns remain about tepid consumption in the world’s top consumer.
Steel demand across the country is seasonally waning as construction activities slow due to cold weather.
“The sharp fall in physical steel prices in the last week of 2017 has encouraged some limited restocking by traders, which stabilized the physical market, but the overall demand remains weak and commercial inventories keep rising,” said a trader in Shanghai.
Stockpiles of construction product rebar held by Chinese traders in big cities rose for a second week to 2.973 million tonnes, up 1.5 percent from a week ago, according to data tracked by SteelHome website. SH-TOT-RBARINV
The most active rebar on the Shanghai Futures Exchange rose 2.1 percent to 3,874 yuan ($596.67) a tonne after declining 2.9 percent last week.
Steel mills in 28 major producing cities are cutting production until mid-March as part of the government’s efforts to combat smog, leading them to turn to higher-grade iron ore to reduce pollution while still maximizing output.
Iron ore on the Dalian Commodity Exchange closed the first trading day up 2.6 percent at 543.5 yuan a tonne.
Coke rose 1.3 percent to 2,014.5 yuan a tonne, while coking coal jumped 1.8 percent to 1,338 yuan.
Iron ore for delivery to China’s Qingdao port .IO62-CNO=MB settled almost unchanged at $72.61 a tonne on Dec. 29 from the previous day, according to Metal Bulletin. ($1 = 6.4927 Chinese yuan) (Reporting by Ruby Lian in SHANGHAI and Ryan Woo in BEIJING; editing by Richard Pullin and Biju Dwarakanath)