* High supply of both steel and iron ore in China
* Rebar, iron ore futures end slightly higher for the day
* Spot iron ore headed for second weekly gain (Updates prices)
By Manolo Serapio Jr
MANILA, June 23 (Reuters) - Chinese steel futures edged higher on Friday but still posted a third weekly loss in four, pressured by ample supply at a time when consumption is seasonally weak.
Hot weather and rains in China typically slow down construction activity during summer, limiting demand for steel.
The most-active rebar on the Shanghai Futures Exchange closed 0.6 percent higher at 3,104 yuan ($454) a tonne, after shedding as much as 1.7 percent earlier in the session.
The construction steel product lost nearly 2 percent this week, its third such loss in four weeks.
China produced 72.26 million tonnes of crude steel in May, not far below a record 72.78 million tonnes in the previous month. Analysts say output could remain high this month, which could keep prices under pressure.
The most-traded iron ore on the Dalian Commodity Exchange gained 0.2 percent to end at 434 yuan a tonne, and was flat for the week.
Iron ore supply in China remains high, with stocks of the steelmaking raw material at the country's ports near their highest level in 13 years.
Inventory of imported iron ore at the ports stood at 138.95 million tonnes last week, according to data tracked by SteelHome. The stockpiles reached 140.05 million tonnes the week before, the most since 2004.
Spot iron ore prices managed marginal gains this week, with the benchmark hitting near $57 a tonne, its highest in two-and-a-half weeks.
CMC Markets analyst Ric Spooner said the recent improvement in spot iron ore prices is a "minor relief."
"However, it would take a break above chart resistance at around $60 to indicate markets were having a major rethink on the threat posed by forecast supply increases," he said in a note.
Iron ore for delivery to China's Qingdao port .IO62-CNO=MB slipped 0.5 percent to $56.53 a tonne on Thursday, according to Metal Bulletin. It has gained 1.4 percent so far this week, on track for its second weekly increase. ($1 = 6.8382 Chinese yuan) (Reporting by Manolo Serapio Jr.; Editing by Sherry Jacob-Phillips)