* Biggest rise since June 2012, up 1.4 percent MEXICO CITY, July 12 (Reuters) - Mexican industrial output rose at its fastest pace in nearly a year in May on stronger manufacturing and more robust construction activity. Compared to the previous month, May industrial activity rose 1.4 percent, well above expectations in a Reuters poll for no change and a downwardly revised 1.76 percent contraction in April, the national statistics agency said on Friday. May's growth was the strongest since June last year. Mexico's factories move in near lock step with U.S. manufacturers, who posted growth in June that bodes well for Mexico. Recent U.S. job growth should also support demand for Mexican-made goods. Manufacturing, which provides the bulk of Mexico's non-oil exports, rose 0.98 percent compared to last month, the biggest rise since last September, while construction grew 2.51 percent compared to April. Solid U.S. demand supported Mexican factories amid sluggish global growth last year, allowing Latin America's No. 2 economy to notch 3.9 percent growth in 2012, but the pace of expansion is seen slowing to 3.1 percent this year. Industrial output rose 0.5 percent in May from a year earlier, in line with expectations and below April's 3.3 percent expansion.