EGYPT and Turkey yesterday held talks on the conflict in Libya, where they back competing factions, on Syria and the security situation in the eastern Mediterranean, in a push to rebuild their fractured relations. The discussions, held over two days and led by deputy foreign ministers, were the first high-level public talks for years between the two powers, who fell out over issues including opposing positions on political Islam and maritime borders. Turkey has been striving to mend fences with several U.S.-allied Arab states including Egypt. Egypt has so far responded cautiously to Turkish overtures. "The discussions were frank and…