* Rebar, iron ore futures rise about 1 pct
* Order books full at many Chinese steel mills -CRU
By Manolo Serapio Jr
MANILA, Aug 10 (Reuters) - Chinese steel futures rose to trade near a 4-1/2-year high on Thursday as investors remained bullish ahead of production cuts in the world's top steel producer.
Demand remained strong, encouraging steel mills to keep offer prices high. Iron ore futures also climbed.
The most-active rebar on the Shanghai Futures Exchange was up 1 percent at 3,966 yuan ($595) a tonne by 0225 GMT. The construction steel product hit a session high of 3,993 yuan, close to Monday's peak of 4,013 yuan which was the strongest level since March 2013.
"The order books are full at many mills through August so they're very aggressive in asking for high prices from customers," said Richard Lu, analyst at CRU consultancy in Beijing.
"I don't expect prices to collapse quickly."
China's bid to curb steel production by as much as 50 percent in major producing areas such as Hebei province during winter spurred a rally in steel prices this week.
In Hebei, steelmakers are required to comply with state- and province-level emission restrictions by Sept. 1 or they will be shut down, the Hebei Province Environmental Protection Bureau said on Tuesday.
The most-traded iron ore on the Dalian Commodity Exchange rose 1.2 percent to 565 yuan ($84.83) per tonne.
While overall iron ore supply in China is high, particularly at its ports, traders said availability of high-grade raw material is limited. Steel producers are increasingly opting for higher grade iron ore to boost efficiency.
"There isn't a lot of high-grade around and Chinese mills are preferring high-grade because they want to produce more with steel prices rising," said a trader in Jinan in China's eastern Shandong province.
Stockpiles of imported iron ore at China's ports stood at 139.15 million tonnes on Friday, according to data tracked by SteelHome. SH-TOT-IRONINV
That was not far below the record 141.45 million tonnes reached in June, but the Jinan-based trader said only about a fifth of that inventory is comprised of high-quality Australian iron ore fines. ($1 = 6.6627 Chinese yuan) (Reporting by Manolo Serapio Jr.; Editing by Richard Pullin)