LIMA, June 18 (Reuters) - A group of retired officers has suggested Peru"s military should refuse to recognize socialist candidate Pedro Castillo if he is declared winner of the country"s presidential election if fraud allegations are not investigated, according to a letter circulated widely on social media on Friday. Interim president Francisco Sagasti confirmed the letter, which was posted on Twitter and Facebook, arrived at the general headquarters of the armed forces, bearing the names of at least 80 retired military personnel. Sagasti said he had ordered an investigation into what he said could be "harmful conduct" against the rule of law and insisted the armed forces should remain neutral. Peru held a second round of its presidential elections on June 6, with Castillo ahead of conservative candidate Keiko Fujimori by a razor thin margin, according to the electoral office"s vote count completed on Tuesday. The winner has not yet been officially declared because the party of Fujimori, the eldest daughter of imprisoned ex-president Alberto Fujimori, has asked for the annulment of some 900 voting tables where she alleged, without publicly providing evidence, that fraud was committed. Friday"s letter appealed to military chiefs to "act rigorously" and "remedy" the "demonstrated irregularities" that took place during the vote or risk having an "illegal and illegitimate" commander in chief at the helm of the country. The tight election has deeply divided citizens of the world"s second-largest copper producer. Protest marches by supporters of both candidates take place almost daily in downtown Lima, calling for a swift resolution and respect for the popular will. Castillo, 51, obtained 50.125% of the votes in the second round, a lead of 44,058 votes over Fujimori, who according to her lawyers seeks to nullify some 250,000 votes, mostly cast in poor rural areas which constitute Castillo"s support base in contrast to her largely urban one. Castillo"s ascent to within a whisker of high office, and his plans to redistribute wealth, hike mining taxes and rewrite the constitution, have alarmed Peru"s elite and foreign investors. The Armed Forces played a key role in the career of Alberto Fujimori, backing him when he shut down Congress in 1992 and assumed the broad powers of an authoritarian government. Reporting by Marco Aquino, writing by Aislinn Laing Editing by Sonya Hepinstall