* Nikkei trades above 13,500 for first time since June 11 * Strong industrial production data, CPI help mood * Exporters gain as dollar stays above 98 yen * All sectors in positive territory By Ayai Tomisawa TOKYO, June 28 (Reuters) - Japan's Nikkei share average rose to a two-week high on Friday, helped by optimism that the Federal Reserve will not rapidly rein in its stimulus measures and by encouraging domestic economic data. The Nikkei rose 2.3 percent to 13,516.43 points by midmorning trade, its highest since June 11. Japan's core consumer prices were flat in May compared with a year earlier, marking the first time they have stopped falling in seven months, government data showed on Friday. Meanwhile, Japanese industrial output rose 2.0 percent in May from the previous month, up for the fourth consecutive month, a sign that a pick-up in exports is underpinning factory output and the broader economy. The figure was better than a market consensus of a 0.2 percent increase. "Investors are cheered by the better data and see that Abenomics is being effective for the economy," said Takuya Takahashi, an analyst at Daiwa Securities. The Topix gained 2.3 percent to 1,123.91. The weak yen is also helping the mood, and exporters attracted buyers as the dollar is comfortably trading above 98 yen. Toyota Motor Corp gained 1.5 percent, Sony Corp added 1.7 percent, and Nikon Corp advanced 1.4 percent. The benchmark Nikkei has dropped 15 percent since reaching a 5-1/2-year high on May 23, hurt by slowing growth in China, fears of a pullback in U.S. stimulus and disappointment over the Japanese government's recently announced growth strategy. However, it is still up about 30 percent this year on the back of Prime Minister Shinzo Abe's expansionary policy, weaker yen as well as the Bank Of Japan's sweeping monetary easing. Market players said that the Nikkei may be resilient as overseas headwinds such as worries about the U.S. Fed's plan to trim its stimulus and fears for the stability of the Chinese banking system are easing. But they added that volume may stay subdued in the absence of firm catalysts. "Buying may be contained in short-covering," said Mitsushige Akino, chief fund manager at Ichiyoshi Asset Management. "The market wants to see April-June results, and investors want to see the results of the upper house election to trade proactively." On Thursday, U.S. stocks rose after three Fed policymakers sought to downplay the notion that the central bank would bring an imminent end to its bond-buying programme. All of Topix's 33 subsectors were in positive territory.