LIMA, July 14 (Reuters) - A bid by conservative Keiko Fujimori to flip the result of Peru"s June 6 presidential election looks to have run out of road, setting the stage for socialist rival Pedro Castillo to be confirmed the Andean country"s next leader. The run-off vote had ended with political outsider Castillo ahead by a narrow margin of 44,000 votes, but the official result has been delayed by challenges from Fujimori to annul some ballots on claims of fraud, despite little evidence. Those challenges have now been fully reviewed and rejected by electoral authorities, a lawyer for Fujimori"s conservative Popular Force party told Reuters on Wednesday. Fujimori"s party plans to challenge more ballots from some electoral districts, but those total only around 5,400 votes. That would not be enough to change the result of the election, although it could delay the announcement and complicate the transfer of power to Castillo. "At the moment the numbers favor him, with about 40,000 votes," the lawyer Julio César Castiglioni told Reuters by phone. He said that once the process before the National Elections Jury has been exhausted, there was no plan by the Fujimori campaign to take further legal action. The Organization of American States, European Union, Canada, Britain and the U.S. State Department have all stated that the elections in Peru were clean. If confirmed in time, Castillo would take office on July 28 for a five-year term as leader of the world"s second largest copper-producing nation. A spokesman for the National Elections Jury, which oversees the electoral process, said earlier this week that it hoped to proclaim the winner next week. Castillo, a 51-year-old former school teacher and the son of peasant farmers, has pledged to redraft the constitution and hike taxes on mining firms. He has though softened some of his rhetoric in recent weeks and brought on more moderate economic advisers to help calm investor and market fears. He has publicly asked the well-respected central bank head to stay in his role. The tightly contested vote has deeply divided Peru and put a spotlight on regional and social tensions, with poorer rural voters backing Castillo and wealthier urban Peruvians favoring Fujimori.