UPDATE 2-Japan May crude steel output up 13 pct from April

* Slight recovery in demand seen - industry body

* First month-on-month rise in two months

* Eighth straight month of declines year-on-year

TOKYO, June 18 (Reuters) - Japan's crude steel output in May rose 13 percent from April as demand from makers of cars and household electronics edged up, an industry body said on Thursday.

It is the latest sign that the industry is emerging from the worst of the recession, but prospects for recovery are still dim as the improvement is seen as a rebound from sharp inventory adjustments made from late last year to early this year, market watchers said.

The Japan Iron and Steel Federation said crude steel output in May rose 750,000 tonnes to 6.49 million tonnes. It was the first month-on-month rise in two months, though the output increase in March was due to February having fewer days.

For historical crude steel output data click: here

"Drastic output cuts at steelmakers have run their course," said an official at the Japan Iron and Steel Federation.

"There is a slight rise in demand from carmakers and household electronics makers thanks to progress in inventory adjustments, while a rundown in steel stocks helped," he said.

Output in May was down 38.5 percent from a year earlier, falling on a year-on-year basis for the eighth straight month.

"It's not yet clear when and whether real demand will recover," said Masayuki Kubota, a senior fund manager at Daiwa SB Investments.

"But the government's massive spending and credit easing will help prop up real demand, and that will help steelmakers to ease production cuts further."

Japan's top two steelmakers, Nippon Steel Corp (5401.T) and JFE Holdings Inc (5411.T), have been operating at 55-66 percent capacity in the face of an economic slump that has forced automakers and other customers to cut orders.

A Nippon Steel executive told Reuters this month he expected the capacity run rate to rise to nearly 70 percent in July-September but that the recovery still lacked strength.

Japan's industrial output posted the biggest monthly gain in more than half a century in April, figures showed last week, while the Bank of Japan upgraded its assessment of the economy this week.

The central bank warned, however, that the outlook was highly uncertain with companies not yet convinced that a recovery, if any, would be sustainable. (Reporting by Yuko Inoue; Editing by Michael Watson)