* Chinese markets shut on Oct. 3-7 for National Day break
* ANZ says now sees China's 2016 steel output up, not down
* Steel demand seen recovering on housing, infrastructure boost (Updates prices)
By Manolo Serapio Jr
MANILA, Sept 30 (Reuters) - Chinese steel and iron ore futures pulled back on Friday as investors locked in recent gains ahead of a week-long holiday although some expect demand for the two commodities to bounce back.
The most-traded iron ore on the Dalian Commodity Exchange closed down 3.2 percent at 404.50 yuan ($61) a tonne, after touching a three-week high of 426.50 yuan on Thursday.
The retreat in iron ore followed losses in steel prices. The most-active rebar on the Shanghai Futures Exchange fell 2.3 percent to 2,253 yuan per tonne, after scaling a two-week peak on Monday.
There was limited activity in physical markets ahead of China's National Day holiday when markets will be shut between Oct. 3 and 7.
There were a few deals in the spot iron ore market this week, traders said, but they said most steel mills have either enough stocks of the raw material or have replenished inventories well ahead of the holiday.
China's steel demand should strengthen after the week-long break on the back of relatively strong investment in the housing and infrastructure sectors, said Daniel Hynes, senior commodity strategist at ANZ.
ANZ is now looking at China's crude steel production to rise 2 percent this year versus an earlier forecast for a decline of 5 percent.
"With the construction cycle lasting approximately 12 to 18 months, building completions are likely to stay relatively strong through 2017," said Hynes.
"This should be positive for steel demand, and thus iron ore prices for the remainder of the year."
Iron ore for delivery to China's Tianjin port .IO62-CNI=SI rose 0.4 percent to $56.10 a tonne on Thursday, according to The Steel Index.
The spot benchmark has lost nearly 5 percent in September, on track for its first monthly fall in four.
$1 = 6.6702 Chinese yuan Reporting by Manolo Serapio Jr.; Editing by Christian Schmollinger and Amrutha Gayathri