* Steel output cuts, firm demand boost Shanghai futures
* Iron ore falls as steel output curbs dent appetite
SHANGHAI, March 2 (Reuters) - Chinese steel futures rose on Thursday after two consecutive days of losses, with recovering demand and production curbs in the world's top producer of the metal underpinning prices.
Steel demand in China improved in March as construction activities picked up amid warm weather, while steel mills in some northern regions were ordered to cut output to reduce smog. Rebar is mainly used for construction.
"Rebar is the most safe commodity futures for now as rebar supplies have been hard hit by the government's environmental crackdown, and now demand is increasing," said Li Wenjing, an analyst with Industrial Futures in Shanghai.
However, she also expects the gains to ease after the production cuts in Tangshan, a leading steel-producing city, end in mid-March.
The most active rebar on the Shanghai Futures Exchange climbed 0.5 percent to 3,533 yuan ($513.26) a tonne by the midday break.
Iron ore on the Dalian Commodity Exchange dipped 0.2 percent to 693.5 yuan a tonne.
Traders said prices of iron ore, a main steelmaking ingredient, have been supported by demand for steel and its strengthening prices, but that gains have been capped due to pressure from the production cuts at mills.
On the Dalian Commodity Exchange, coking coal rose 0.8 percent to 1,308 yuan a tonne, and coke futures gained 1.3 percent to 1,802 yuan a tonne.
$1 = 6.8835 Chinese yuan Reporting by Ruby Lian and Josephine Mason; Editing by Tom Hogue