* Nikkei falls 2 pct to a six-month low
* Sony drops below 1,000 yen for first time since 1984
* Canon underperforms after JPMorgan downgrade
By Dominic Lau
TOKYO, June 4 (Reuters) - Japan's shares fell sharply in early trade on Monday, with the Topix index falling to a near three decades low, as disappointing U.S. jobs data added to concerns over a slowing Chinese economy and a deepening euro zone debt crisis.
The broader Topix index lost 2.1 percent to 694.42, a level not seen since late 1983. Last week, it fell for the ninth straight week, marking its longest such run since 1975.
The Nikkei dropped 2 percent to 8,271.07 to a six-month low.
The Nikkei has fallen 19.3 percent since hitting a one-year high on March 27 on concerns over a deepening euro zone debt crisis and slowing global growth. If the benchmark were to drop to around 8,200, it would technically enter bear market territory.
"The investment sentiment is quite weak, so there's a possibility of a further sell-off. The Nikkei can go down more, that's a possibility," said Hisao Matsuura, equity strategist at Nomura.
"From a valuation view point, it is attractive, and investors almost seem to agree, but they don't want to buy now."
The Topix's 12-month forward price-to-earnings ratio has fallen to 10.9, a level not seen since November 2008, data from Thomson Reuters Datastream showed.
U.S. job growth braked sharply for a third straight month in May and the unemployment rate rose for the first time in nearly a year, raising the chance of further monetary stimulus from the Federal Reserve to support the sputtering recovery.
"The U.S. employment was clearly disappointing ... This is the new normal recovery type, less employment," said Shun Maruyama, chief Japan equity strategist at BNP Paribas.
He said the market was likely to rebound in the near-term led by short-covering ahead of the European Union summit on June 28-29, however.
The Nikkei was in deep in "oversold" territory, with its 14-day relative strength index at 23. Thirty or below is deemed oversold.
The prospect of another round of stimulus by the U.S. Federal Reserve weighed on the dollar against the yen, putting added pressure on Japanese exporters, who are faced with weaker global demand for their products.
Sony Corp, the maker of Walkman and Playstation, eased 1.3 percent to 1,000 yen after falling below that level for the first time since 1984 according to Reuters data.
Canon Inc dropped 3.7 percent to 2,938 yen, breaking the 3,000 level for the first time since July 2009 after JPMorgan downgraded the camera and printer maker's rating by two notches to "underweight" from "overweight".
Automakers Toyota Motor Corp, Nissan Motor Co and Mazda Motor Corp shed between 3.1 and 7.3 percent.
Renesas Electronics Corp jumped 15.6 percent after trouble chipmaker asked major shareholders - Mitsubishi Electric Corp, Hitachi Ltd and NEC Corp - for support of its restructuring plan.
Trading volume on the Topix after the halfway point was relatively light, at 41.6 percent of its full daily average for the past 90 days.
Taiyo Yuden also bucked the weak trend, up 2.3 percent after a trader said the electronics parts maker posted surprisingly strong orders in May.