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UPDATE 1-Japan industrial output increase hints at more stable growth

(Adds breakdown of output)

* June factory output +1.6 pct vs f'cast +1.7 pct

* Manufacturers expect output to rise in July and Aug

* Rising output would support economic growth

TOKYO, July 31 (Reuters) - Japan's factory output rebounded in June from a decline in May as production of cars and industrial chemicals increased, suggesting economic expansion may be on a more stable footing.

Industrial output rose 1.6 percent in June from the previous month, just below the median estimate for a 1.7 percent increase and following a 3.6 percent decline in May.

Manufacturers forecast a steady increase in output in coming months, offering further evidence that firm overseas demand and gains in consumer spending could support overall growth in Japan's economy. Output in the transport sector rose 4.2 percent in June, rebounding from a 13.0 percent tumble in the previous month, as output of passenger cars and automobile recovered.

Output of chemicals rose 3.4 percent in June, also a rebound from a 2.2 percent decline in May.

Manufacturers surveyed by the ministry expect output to rise 0.8 percent in July and 3.6 percent in August.

The positive output reading follows data last week showing the biggest increase in household spending in almost two years and an increasingly tight labour market, building optimism that the economy will maintain its upward momentum. (Reporting by Stanley White; Editing by Eric Meijer)