* KOSPI eyes 7th day of rise, longest streak in 2-1/2 yrs
* Won on track to snap winning streak
By Jungmin Jang
SEOUL, April 3 (Reuters) - South Korean shares rose to three-month highs on Thursday morning, encouraged by news of stimulus steps from China to bolster growth and on solid U.S. data, though the won slipped on the back of a well-bid dollar.
China acted for the first time this year to steady its sagging economy by cutting taxes for small firms, providing much needed relief to global markets worried about a deepening slowdown in Asia's economic powerhouse.
Adding to the improved mood, data in the U.S. showed companies stepped up hiring in March for a second straight month.
The Korea Composite Stock Price Index (KOSPI), which has been partly supported in recent sessions on the China stimulus hopes, was up 0.3 percent at 2,003.23 points as of 0231 GMT. It earlier reached a high of 2,007.88, the highest level since Jan. 2.
The gains kept the KOSPI on track for a seventh-straight winning session, its longest since an eight day streak in October 2011.
"The market has been moving in line with regional markets on cheap valuation as global macro-economic condition continues to improve, but for a longer-term rise, it needs to demonstrate its profitability," said Hana Daetoo Securities analyst Chang Hee-jong.
Chang was referring to the upcoming corporate earnings results for the January-March quarter, which analysts say could determine the short-term outlook for the KOSPI.
Traders also say the market could be ripe for a correction as the main index has moved deep into "overbought" territory. Its 14-day relative strength index stood at 77.7, above the 70-mark which is deemed overbought and often points to a correction.
Foreign investors purchased a net 147.6 billion won ($139.7 million) worth of KOSPI shares near mid-session, and headed for a seventh straight session of net buying. Foreign net inflow totaled more than 1.5 trillion won during this period,
Market heavyweights Samsung Electronics Co Ltd and LG Display Co Ltd benefited from the foreign buying spree, advancing 2.3 percent and 3.2 percent, respectively.
STX Heavy Industries Co Ltd bucked the broad market by tumbling 7.3 percent, after stock market operator Korea Exchange asked the company to clarify by 0900 GMT media reports of allegations of embezzlement and breach of trust against its former CEO.
Decliners outnumbered advancers 434 to 341.
The KOSPI 200 benchmark of core stocks was up 0.4 percent, while the tech-heavy junior KOSDAQ edged 0.3 percent higher.
In the foreign exchange market, the won eased after the upbeat U.S. private jobs data spurred the dollar, prompting investors to cover recent short positions.
Dealers, however, believe the won could turn around before the close of trading.
"The dollar-long bids seem to be the general thought, but there are uncertainties surround supply and demand," a foreign bank dealer said. "Should dollar selling by exporters or selling related to local stocks flow occur, the direction of dollar-won movement could change in the afternoon."
The local currency was quoted at 1,058.1 against the dollar near mid-day, down 0.1 percent from Wednesday's close of 1,056.6. The won has risen 2.1 percent during its six-session winning streak.
Fixed income assets tracked weakness in the U.S. Treasuries, with June futures on three-year treasury bonds ticking down 0.06 points at 105.63 on offshore selling.
0231 GMT Prev close Dollar/won 1,058.1 1,056.6 Yen/won 10.1790/838 10.1752 *KTB futures 105.63 105.69 KOSPI 2,003.23 1,997.25 * Front-month futures on three-year treasury bonds ($1 = 1056.5500 Korean Won) (Additional Reporting by KyoungHo Lee)