* Annual export falls narrow to China, U.S., Europe
* Economists lukewarm on outlook (Adds export volume details in paragraph 7, sector details in paras 10, 16)
By Stanley White
TOKYO, July 23 (Reuters) - Japan's annual export slide slowed in June from May, trade data showed on Thursday, suggesting that stimulus spending around the world is propping up global demand.
Annual declines narrowed for Japan's exports to China, one of the world's most vibrant economies, as well as to the United States and Europe, boding well for Japanese auto and electric machinery firms.
Still, some economists are lukewarm on the outlook, because once stimulus measures fade, final demand won't be strong enough to pick up the slack.
"The key for the outlook is whether U.S. consumption will pick up, and when. Given the dire job conditions there, we can't expect it to happen soon," said Takeshi Minami, chief economist at Norinchukin Research Institute.
"That might cap Chinese growth and therefore Japanese exports."
The 35.7 percent annual fall in the value of exports in June roughly matched economists' median forecast for a 35.1 percent drop and was smaller than a 40.9 percent decline in May, the Ministry of Finance data showed.
Measured in terms of volume, Japan's exports declined 27.6 percent in June from a year earlier, also slower than the 36.0 percent annual decline in the previous month.
On a seasonally adjusted basis, exports rose 1.1 percent in June from May, for the first gain in two months.
Slowing declines in shipments of steel, semiconductors, car parts and electronic parts to Asia were the main reason Japan's overall exports fell at a slower annual pace in June, a MOF official told reporters at a briefing.
China-bound exports fell 23.7 percent in June from the previous year, smaller than a 29.7 percent drop in May, the trade balance data showed.
Shipments of steel to China fell 19.1 percent in June from a year earlier, almost half the 35.9 percent annual decline in the previous month. Exports of semiconductor parts to China declined 11.0 percent in the 12 months to June, also a much slower pace than a 25.8 percent annual decline the month before.
Japan's exports have benefited from government stimulus in China, whose economy grew a faster-than-expected 7.9 percent in the second quarter from a year earlier due to a surge in state spending and bank lending.
China's imports fell 13.2 percent in June from a year earlier, about half the previous month's 25.2 percent fall, as Beijing pump-primed its economy.
Exports to the United States fell 37.6 percent while those to the European Union were down 41.4 percent, both narrowing their pace of annual declines.
Auto exports to the United States fell at a slower annual rate in June, in another sign that exports are gradually recovering, the MOF official said.
In volume terms, Japan shipped about 124,000 autos to the United States, up from about 83,000 in May, as firms restock inventories, the official said. Shipments to the European Union were around 65,000 units, up from May's 50,000, he said.
The yen slipped to 93.69 yen per dollar after the data from about 93.55, while Tokyo stocks were flat.
Japan's economy is gradually emerging from its worst postwar recession with exports and output on the mend, but production is still down about 30 percent from last year and many manufacturers are considered to be operating below the break-even point.
Unless global demand recovers strongly, Japanese exporters may need to cut more jobs and production facilities, some analysts say.
"Exports are still growing, but it's not like external demand is improving sharply either," said Junko Nishioka, chief Japan economist at RBS Securities.
"Overseas inventories at Japanese firms have declined while demand is slowly recovering, so I expect exports to continue to grow, but I doubt we'll see strong growth like in 2005-2006."
Many economists warn that any economic recovery will be modest as companies have only just started to pass on the pain to households through cuts in jobs and wages. (Editing by Hugh Lawson)