* Steel demand outlook shaky amid summer lull
* Coking coal curbs gains after hitting near one-month top
* China plans to improve iron ore price index (Adds China iron ore index plan, updates prices)
By Manolo Serapio Jr
MANILA, June 22 (Reuters) - Chinese steel futures gave up early gains to end lower for a third session in a row on Thursday as the outlook for demand in the world's top consumer remained weak amid the summer lull.
Hot weather and rains in China typically slow construction activity during summer, curbing demand for steel.
"Our view is that demand is entering a seasonally weak period but supply will remain quite high and that will put prices under pressure," said Kevin Bai, analyst at CRU consultancy in Beijing.
But Bai said spot steel prices could be affected by "short-term speculative behavior in the futures market" which had been quite volatile in recent sessions.
The most-active rebar on the Shanghai Futures Exchange closed down 1 percent at 3,031 yuan ($444) a tonne, after rising as high as 3,123 yuan. The construction steel product touched a three-week high on Monday.
As steel retreated, the most-traded iron ore on the Dalian Commodity Exchange ended 0.1 percent lower at 425.50 yuan a tonne, after climbing as much as 2.9 percent during the session.
Iron ore for delivery to China's Qingdao port .IO62-CNO=MB increased 0.7 percent to $56.82 a tonne on Wednesday, the strongest level since June 2, according to Metal Bulletin.
China is planning improvements to an iron ore price index it launched six years ago, looking to better reflect market dynamics in the world's biggest user of the steelmaking raw material and increase usage by market participants.
China has been pushing for a greater say in pricing iron ore in the global market where buyers and sellers mostly use dollar-denominated index prices from providers such as S&P Global Platts and Metal Bulletin.
Steelmaking coal futures also came off the session's highs on Thursday. Coking coal on the Dalian exchange ended up 1.6 percent at 1,032.50 yuan per tonne. Earlier in the session, it hit 1,058 yuan, its highest since May 26.
Coke rose 1.6 percent to settle at 1,621.50 yuan, off the intraday peak of 1,655 yuan. ($1 = 6.8322 Chinese yuan) (Reporting by Manolo Serapio Jr.; Editing by Richard Pullin and Sherry Jacob-Phillips)