* Shanghai rebar, spot iron ore hit 5-week highs
* China's steel demand solid, continues to pick up -Morgan Stanley
By Manolo Serapio Jr
MANILA, Oct 14 (Reuters) - Shanghai steel futures climbed to five-week highs on Friday and were headed for their biggest weekly gain since at least August amid solid demand that has kept production high and boosted appetite for raw material iron ore.
Spot iron ore, helped by the firmer futures markets for both steel and iron ore, also scaled five-week peaks and was on course for its best week since late July.
Morgan Stanley estimates that China's implied apparent steel consumption in September rose 12.5 percent from a year ago and 2.8 percent from the previous month. The investment bank said the strong double-digit annual growth may be largely due to a low base in September 2015.
"However, the month-on-month growth does suggest that demand remains solid and continues to pick up as we are entering the traditional peak season," Morgan Stanley analysts said in a report.
"We expect the near term steel price to be supported on solid demand and higher raw material costs."
Rebar, a construction steel product, on the Shanghai Futures Exchange was up 1.3 percent at 2,379 yuan ($357) a tonne by 0256 GMT. It hit 2,388 yuan earlier, the highest since Sept. 7.
For the week, rebar has gained as much as 5 percent so far, the most since at least early August.
Iron ore for delivery to China's Tianjin port .IO62-CNI=SI rose 0.2 percent to $56.60 a tonne on Thursday, the highest since Sept. 9, according to data from The Steel Index. The spot benchmark was up 4 percent so far for the week, on track for its biggest such gain since the last week of July.
China's iron ore imports reached 93 million tonnes in September, the second highest on record, as healthy profits pushed steel mills to ramp up steel output.
Chinese mills could not fully digest the strong imports "resulting in stockpiling," Argonaut Securities analyst Helen Lau said, with inventories of the raw material at major ports as of Oct. 7 up 24 percent from a year ago.
"Steel production increases will be lagging behind iron ore supply increases due to China's overcapacity reduction campaign. As a result we expectthe iron ore price to trade below $60/tonne for the rest of the year," Lau wrote in a note.
The most-traded iron ore contract on the Dalian Commodity Exchange climbed to a seven-week high of 434 yuan a tonne on Friday, and was last up 0.7 percent at 429 yuan.
$1 = 6.6685 Chinese yuan Reporting by Manolo Serapio Jr.; Editing by Tom Hogue