CAIRO — Libya’s chief prosecutor says he would establish a fact-finding mission to investigate a meeting last month between the foreign minister of one of the country’s rival governments and Israel’s chief diplomat. Najla Mangoush, the foreign minister of the Tripoli-based government, and Foreign Minister Eli Cohen met in Rome for the first-ever between top diplomats of Libya and Israel. In a terse statement, General Prosecutor Al-Sediq al-Sour says the fact-finding mission would probe violations of Libya’s rules of boycotting Israel and “investigate the extent of damage to Libya’s interests” because of the Mangoush-Cohen meeting. For years, the country has split between the Western-backed government in Tripoli and a rival administration in the country’s east. Each side has been backed by armed groups and foreign governments.