* Nikkei rises 1.3 pct, Topix up 1.2 pct * Sharp down 2.4 pct at midday due to report of Apple cuts * Exporters, economy-sensitive stocks strong By Tomo Uetake TOKYO, Jan 15 (Reuters) - Japan's Nikkei share average climbed 1.3 percent to a 32-month high on Tuesday, driving the benchmark further into "overbought" territory, as persistent weakness in the yen boosts demand for exporters' shares. By the midday break, the Nikkei rose 136.05 points to 10,937.62, setting its sights on the 11,000-mark, a level not seen since late April 2010. It rose 1.1 percent last week to log its ninth straight week of gains and its longest such winning run since 1988. Monday was a public holiday in Japan. "It's because the yen weakened further against dollar over the weekend. We expect the current trend to continue until the Nikkei reaches 11,000 and the yen hits 90. Once it gets there, Tokyo stocks are likely to move in a boxed range," said Naoki Fujiwara, a fund manager at Shinkin Asset Management. Tuesday's rally took the benchmark Nikkei's 14-day relative strength index at 80.4, way above the 70-mark which is deemed overbought and often signals a near-term correction. "Short-term correction is getting more likely given that bullish sentiment ... has become more widespread. In terms of my positioning, I have trimmed down the exposure to stocks which have skyrocketed in the past two months," said Yasuo Sakuma, portfolio manager at Bayview Asset Management. The Nikkei has rallied more than 26 percent over the past two months, spurred by the weakness in the yen after Japan's new leader Shinzo Abe called on the Bank of Japan to adopt aggressive policies to energise the ailing economy, including setting an inflation target of 2 percent. Exporters led the index higher on Tuesday, including Suzuki Motor Corp, Panasonic, Daikin Industries Ltd , Olympus Corp and auto parts maker Denso Corp , which were up between 3 and 9.3 percent. Japanese automakers are aiming to shake off the lingering effects of 2011's earthquake and tsunami, and capitalise on the weakening yen and new products to increase sales in the United States, after a robust 2012. The yen was quoted at 88.80 to the dollar on Tuesday after falling 0.4 percent to a 2-1/2-year low of 89.67 yen in the previous session. The Japanese currency was traded at 118.785 to the euro. As global risk sentiment improved, investors bought growth-sensitive stocks. The sea transport sub-index rose 4.7 percent, making it the best sectoral performer, and the mining sub-index was up 2.6 percent. Stocks expected to benefit from Abe's reflationary policies continued to be in demand. The real-estate sub-index rose 2.5 percent. APPLE SUPPLIERS WEAKER Sharp Corp, however, sagged as much as 7 percent after the Nikkei newspaper said on Monday that Apple Inc has slashed orders with suppliers of LCD panels for the iPhone 5 in the current quarter due to weak demand. Other Apple suppliers in Japan also came under pressure, with Murata Manufacturing Co Ltd down 1.9 percent and Foster Electric Co Ltd off 1.9 percent. The broader Topix gained 1.2 percent to 909.42 in active trade in the morning session, with volume at its full daily average for the past 90 trading days. Japanese equities carry a 12-month forward price-to-earnings ratio of 13, compared with the U.S. S&P 500's 12.9 and the pan-European STOXX Europe 600's 11.4, data from Thomson Reuters Datastream showed.