Chinese iron ore and steel futures surged to three-month highs on Monday as the government-ordered steel production cutbacks led to tighter supplies for some mill products.

The upwards push was led by a big spike in steel prices that follows the global top producer's orders to 28 cities to cut industrial production to battle smog and clean skies.

The most active rebar on the Shanghai Futures Exchange hit a high of 4,104 yuan ($620.50) a tonne, its highest since Sept. 6.

"The production cut has caused supply shortages of some rebar products, while demand has not been affected as much," said a futures analyst in Shanghai.

Iron ore on the Dalian Commodity Exchange followed, rising more than 6 percent to hit 555 yuan a tonne, the highest since Sept. 13.

Spot iron ore for delivery to China's Qingdao port <.IO62-CNO=MB> has also surged, gaining 2.9 percent to $70.11 a tonne last Friday, according to Metal Bulletin.

"Iron ore prices rose above $70 per tonne (CFR China) on demand hopes as stronger steel prices encouraged steel mills in China to boost output," Vivek Dhar, an analyst with Commonwealth Bank of Australia, said in a note.

Steel mills are expected to resume normal production from around mid-March, after the end of the ordered output cuts, about the time when steel demand seasonally picks up.

That's raising expectations that steel mills will restock iron ore early next year.

"Restocking demand also prompted prices (to move) higher with reports of low iron ore inventories at some steel mills in the provinces of Shandong and Hebei," Dhar said.

China's crude steel output is expected to rise 3 percent to 832 million tonnes this year, and by a further 0.7 percent in 2018, as major mills ramp up operations, offsetting impact from the shutdown of outdated plants, said the China Metallurgical Industry Planning and Research Institute.

Iron ore demand in the world's top buyer is expected to rise 1.3 percent to 1.122 billion tonnes this year and dip slightly to 1.12 billion tonnes next year, according to the MPI report.

On the Dalian Commodity Exchange, coking coal futures gained 1.8 percent to 1,417.5 yuan a tonne and coke futures rose 2.4 percent to 2,219 yuan a tonne.