JERUSALEM—Israel’s president handed Prime Minister Benjamin Netanyahu the difficult task on Tuesday of trying to form a government from the country’s splintered parliament, giving the embattled leader a chance to prolong his lengthy term in office while he stands trial on corruption charges. In his announcement, President Reuven Rivlin acknowledged that no party leader had the necessary support to form a majority coalition in the 120-seat Knesset. He also noted that many believe Netanyahu is unfit to serve as prime minister in light of his legal problems. Nonetheless, Rivlin said that there was nothing in the law preventing Netanyahu from holding that office. After consulting with the 13 parties in the newly elected parliament, Rivlin said that Netanyahu had the best chance of any candidate forming a new government. “I have decided to entrust him with the task,” Rivlin said from Jerusalem. “This is not an easy decision on a …