* Nikkei falls 2.1 pct to a six-month low
* Sony drops below 1,000 yen for first time since 1984
TOKYO, June 4 (Reuters) - Japan's shares fell sharply in early trade on Monday, with the Topix index falling to a more than 28-year 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 693.35, 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 2.1 percent to 8,267.31 to a six-month low.
The Nikkei has fallen 19.4 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."
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 prospect of another round of stimulus by the Fed weighed on the dollar against the yen, putting added pressure on Japanese exporters, who are already faced with weaker global demand for their products.
Sony Corp, the maker of Walkman and Playstation, eased 1.5 percent to below 1,000 yen for the first time since 1984 according to Reuters data, while industrial robot maker Fanuc Corp, Canon Inc and TDK Corp dropped between 2.6 and 4.2 percent.
Toyota Motor Corp fell 3.5 percent, Nissan Motor Co lost 2.9 percent and Mazda Motor Corp shed 5.2 percent.
Taiyo Yuden bucked the weak trend, up 1.7 percent after a trader said the electronics parts maker posted surprisingly strong orders in May.