* Average daily steel output eases from Apr, but still strong
* Steelmakers keep high output, lured by profit
* Output seen falling in June as demand slows, prices fall (Adds comment, background)
By Ruby Lian and Fayen Wong
SHANGHAI, June 13 (Reuters) - China's crude steel output hit a record of 70.43 million tonnes in May, up 2.6 percent from a year ago, government data showed on Friday, as steel mills in the world's biggest producer looked to meet strong demand.
Steel demand in China traditionally improves in the second quarter as construction activity picks up along with warmer weather, but the slowing economy and weak property sector is expected to curb demand growth and push mills to cut output in coming months.
May's output rose 2.3 percent from April and trumped the previous record of 70.25 million tonnes hit in March. Output for the first five months of the year rose 2.7 percent to 342.52 million tonnes from the same period last year, data from the National Bureau of Statistics showed.
The average daily crude steel output fell to 2.272 million tonnes in May from a record 2.295 million tonnes seen in April. It has stood above 2.20 million tonnes so far this year.
A rapid fall in iron ore prices .IO62-CNI=SI, which have lost about one third and hit a 21-month low, has also helped steel mills to generate a profit of about 50-150 yuan ($8-24.18) a tonne, encouraging them to keep production high, traders said.
But steel demand is seasonally weaker in China during the summer months that start from July as construction activity slows, while steel prices have kept falling, forcing a few small mills starting to scale back output in June.
"Falling daily output rates through May (CISA members) and very weak property construction forward indicators point to growing downside risks for Chinese steel demand and output from the second half into 2015," Lachlan Shaw, a senior analyst with CBA, said in a research note.
Shaw has downgraded Chinese steel output growth to 2 percent from 3 percent this year. Annual growth was 7.5 percent last year.
Steel prices fell 5 percent in May and have lost 18 percent this year.
Output at China's large steelmakers -- members of the China Iron & Steel Association (CISA) -- fell to 1.767 million tonnes between May 21-31, the second consecutive fall. ($1 = 6.2031 Chinese Yuan Renminbi) (Reporting by Ruby Lian and Fayen Wong; Editing by Himani Sarkar)