* Nikkei and Topix both rise 1.2 pct * Fast Retailing up, ahead of Uniqlo June same-store sales By Dominic Lau TOKYO, July 2 (Reuters) - The Nikkei share average climbed above 14,000 points for the first time in nearly five weeks on Tuesday as encouraging U.S. manufacturing and construction data added to signs of an improving economy, which is Japan's biggest export market. The Nikkei gained 1.2 percent to 14,020.56 by midmorning, heading for a fourth straight day of gains - its longest winning streak since mid-May, just before a sharp sell-off that drive the index into bear market territory at one point. "People are kind of taking off their downside strategies, so that's helping the upside a little bit," a senior trader at a foreign bank said, referring to derivative trades among hedge funds. "People are kind of looking at things glass half full, glass half empty in China and emerging markets." The strong U.S. data lifted the dollar to a four-week high of 99.870 yen on Monday. The Japanese currency was last traded at 99.605 to the greenback on Tuesday. Currency-sensitive exporters were in demand as the yen weakened. Toyota Motor Corp rose 1.8 percent, and was the second-most traded stock on the main board by turnover, while Mazda Motor Corp and Honda Motor Co, were also heavily traded, advancing 3.2 and 2.2 percent, respectively. U.S. manufacturing expanded last month, rebounding from an unexpected contraction in May, but hiring in the sector was the weakest in nearly four years, which could make the Federal Reserve think twice about how soon to scale back its stimulus. A separate report also showed construction spending neared a four-year high in May. Other gainers in Tokyo included index heavyweight Fast Retailing, up 0.9 percent, ahead of the monthly same-store sales for its Uniqlo casual clothing chain in Japan. The broader Topix index rose 1.2 percent to 1,164.57 on Tuesday morning, with volume at 23 percent of its full daily average for the past 90 trading days. The benchmark Nikkei had fallen as much as 22 percent from a 5-1/2 year peak hit on May 23 on concerns over the Fed paring its stimulus, a slowdown in China - Japan's second-largest export market - and disappointment over Prime Minister Shinzo Abe's growth strategy to revive the economy. But it has since rebounded from a two-month low reached on June 13. The Nikkei is up 13 percent since the Bank of Japan announced radical monetary stimulus on April 4 and has risen 35 percent this year. As the market regained its confidence, real estate companies , which have rallied hard until the sell-off in May, were back on investors' radar, up 3.9 percent on Tuesday. The sector's 12-month forward price-to-book ratio slipped to 2.1 from a six-year high of 2.8 touched in mid-May, according to Thomson Reuters Datastream. That compared with Japanese equities' 1.1.