TOKYO, July 2 (Reuters) - Japan's Nikkei share average is expected to open higher on Tuesday and may test 14,000, a level not seen since late May, as U.S. manufacturing and construction data added to signs of an improving economy. The Nikkei is likely to trade between 13,800 and 14,000, strategists said, after advancing 1.3 percent to 13,852.50 on Monday to hit a four-week high and mark a third straight gain - its longest winning streak since May. The broader Topix index gained 1.5 percent to 1,150.70. Nikkei futures in Chicago closed at 13,915 on Monday, up 0.3 percent from the Osaka close of 13,870. 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. 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 99.660 to the greenback on Tuesday. "We will likely continue to test strong levels," said Kenichi Hirano, operating officer at Tachibana Securities. "A weaker yen has become the normal condition, and stock prices are showing a tendency to gradually rise." "Sentiment has improved in the Tokyo stock market. Could this be the beginning of the second round of gains from Abenomics?" 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 Federal Reserve 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 12 percent since the Bank of Japan announced radical monetary stimulus on April 4 and has risen 33 percent this year. > S&P 500 extends gains into year's 2nd half on solid data > Dlr drops vs euro; yen down on global manufacturing data > Bonds gain as ISM data fuels Fed speculation > Gold starts Q3 with short covering rally > Oil gains, Brent-U.S. crude spread hits 2-1/2 year low STOCKS TO WATCH --SUMITOMO HEAVY INDUSTRIES LTD Sumitomo Heavy President Shunsuke Betsukawa said the company will decide the fate of its shrinking shipbuilding business this fiscal year, adding the business is small and that it is not considering a merger or integration with another company, the Nikkei newspaper said.