Japan's economy shows weakness, govt slashes view for 3rd month

* Govt cuts view on factory output for 3rd month in row

* Territorial spat between Japan and China may hit sales

* Business mood worsens, especially among manufacturers

By Kaori Kaneko

TOKYO, Oct 12 (Reuters) - Japan's government downgraded its view of the economy for the third month in October as worries about Europe's debt crisis and China's slowdown intensified, adding risk to the growth outlook.

Slackening overseas demand and thus weak exports prompted the government to lower its assessment on factory output for the third straight month.

"The economic recovery has had a weak tone recently due to a slowdown in the global economy, although some steadiness is still shown," the Cabinet Office said in its latest monthly report on Friday.

The Cabinet office downgrade followed the Bank of Japan's warning last week that economic activity was levelling off, offering a slightly bleaker view from the previous month.

The Cabinet Office said factory output is decreasing, but maintained its view of exports as weak in tone.

The latest data showed Japan's industrial production fell to a 15-month low in August on sagging sales to top export market China and business confidence dented by euro zone crisis.

The government also cut its assessment of corporate sentiment for the first time since December last year, noting big companies were cautious, particularly manufacturers.

The BOJ's tankan business sentiment survey showed the mood among big manufacturers worsened in the three months to September and will stay gloomy.

The government is cautious about the impact from tension between Japan and China over the islands in the East China Sea known as the Senkaku in Japan or Diaoyu in China.

The territorial dispute sparked anti-Japan demonstrations in China and calls for boycotts of Japanese goods.

"Trouble stemming from the Senkaku islands is affecting businesses including the auto sector, which would also impact other related industries such as materials and iron and steel ," said Minoru Masujima, director of macroeconomic analysis at the Cabinet Office.

The government still projects the economy will likely return to a recovery path, but uncertainty about the global economic outlook remains prevalent, particularly the prospects of Europe and China.

(Editing by Eric meijer)