CAIRO  - Egypt and Turkey on Thursday 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 in-depth. They addressed bilateral issues as well as a number of regional issues, in particular the situation in Libya, Syria, Iraq, and the need to achieve peace and security in the Eastern Mediterranean region," a joint statement said.

"The two sides will evaluate the outcome of this round of consultations and agree on the next steps."

Turkey is ready to hold a tripartite meeting between Turkish, Egyptian and Libyan officials to agree on disputed issues in Libya including the presence of foreign fighters, two Egyptian intelligence sources said.

Turkey said on Thursday it agrees that all foreign mercenaries in Libya need to leave the country, but Ankara has a bilateral agreement with the Libyan government for its troops to be stationed there.  

The Turkish delegation also told Egyptians that Ankara could not hand over Muslim Brotherhood leaders wanted by Egypt, adding that most of those leaders had now legalized their residency in Turkey, the sources said.

Relations between the regional powers have been tense since Egypt's army toppled a democratically elected Muslim Brotherhood president close to Turkish President Tayyip Erdogan in 2013.

Both countries expelled ambassadors and Erdogan described Egyptian President Abdel Fattah el-Sisi as a tyrant.

Turkey says it remains opposed to the Muslim Brotherhood being declared "terrorists" by Egypt, despite asking Egyptian opposition television channels operating on its territory to moderate criticism of Sisi's government.  

Turkish officials did not comment on the content of the talks. However, Turkish Vice President Fuat Oktay said Ankara is fully open to improve its ties with every country in the region, not just Egypt.

"So Egypt and Turkey moving together will provide serious contributions to the region's peace and development. God willing, we will see this in the coming period," he said during an interview with broadcaster NTV.

(Reporting by Aidan Lewis, Ahmed Mohamed Hassan, Alaa Swillam and Mahmoud Mourad in Cairo Additional reporting by Tuvan Gumrukcu in Ankara Editing by Andrew Cawthorne, Mark Heinrich, Alexandra Hudson) ((Aidan.Lewis@tr.com; +20-1001174410;))