* Falling open interest points to short covering
* Sept iron ore open interest hit 8-week low on Monday
* Shanghai rebar extends gains for the second day
BEIJING, June 27 (Reuters) - Chinese iron ore prices rallied more than 4 percent on Tuesday and were on track for their biggest one-day gain in a month as investors bet on rising demand as steel mills boost output, prompting another rash of short covering
The most-traded iron ore contract on the Dalian Commodity Exchange rose as much as 4.1 percent to 449 yuan ($65.64) a tonne in morning trade, its highest since May 31. Iron ore was at 443.5 yuan at 0450 GMT.
The most-active steel futures rose 1.8 percent to 3,171 yuan per tonnes.
"High margins after the government's effort to eliminate low-grade steel are enticing mills to produce more steel, which increases the need for iron ore," said Zou Mingdong, Shanghai-based steel manager at Zhongcai Merchants Investment Group.
"However, the rising price doesn't change the fundamental situation of oversupply and weak demand."
Margins for ferrous metallurgy and the steel rolling business jumped 93.5 percent in the first five months this year, compared with same period in 2016, data from National Statistics Bureau showed on Tuesday.
"High margins may not last for long due to unpromising demand expectations and resumed capacities in mills," said Zou.
The crackdown on low-end steel production has been in focus recently ahead of a June 30 deadline for mills to halt induction furnaces producing rebar used for construction purposes.
Shutting low-quality steel furnaces is part of China's years-long effort to cut excess capacity and tackling pollution.
"Two decisive battles in the steel industry this year are thoroughly eliminating low-grade rebar and preventing (indusction furnances) from reopening," said Liu Zhenjiang, secretary general at China Iron and Steel Association, at an industry meeting last week in remarks published on Monday.
Open interest in the most-active iron ore contract on Monday fell 56,000 lots to 1.799 million lots, the lowest in nearly eight weeks, reflecting short covering as investors covered bearish bets.
Last week, stocks of imported iron ore at China's ports rose to 141.5 million tonnes, the highest since 2004, according to data tracked by SteelHome. ($1 = 6.8408 Chinese yuan renminbi) (Reporting by Muyu Xu and Josephine Mason; Editing by Richard Pullin)