ISTANBUL, Aug 18 (Reuters) - Regional rivals Turkey and the United Arab Emirates have made progress in improving relations, which could lead to significant UAE investment in Turkey, President Tayyip Erdogan said on Wednesday after a rare meeting with a senior UAE official. Ankara has moved to ease tensions with several Arab powers over the conflict in Libya, internal Gulf disputes and rival claims to Eastern Mediterranean waters. Erdogan held talks in Ankara on Wednesday with UAE National Security Adviser Sheikh Tahnoun bin Zayed Al Nahyan which also focused on economic cooperation. "We discussed what type of investment could be made in which areas," Erdogan said in a television interview. The two countries, which backed rival sides in Libya"s conflict, have been bitter rivals for regional influence. Emirati official Anwar Gargash, diplomatic adviser to UAE President Sheikh Khalifa bin Zayed Al Nahyan, described Wednesday"s meeting as "historic and positive". "The UAE continues to build bridges...", he tweeted. "Prioritising prosperity and development drives both our domestic and foreign policy." Turkey last year accused the UAE of bringing chaos to the Middle East through interventions in Libya and Yemen, while the UAE and several other countries criticised Turkey"s military actions. Erdogan said he hoped to talk with the UAE"s de facto ruler, Abu Dhabi Crown Prince Mohammed bin Zayed Al Nahyan, and for closer economic ties in talks that the heads of Turkey"s Wealth Fund and investment support agency would pursue. "If they continue in a good way with their counterparts, I believe the United Arab Emirates will make serious investments in our country in a very short time," Erdogan said. Wednesday"s meeting came after similar overtures this year by Ankara towards Egypt and Saudi Arabia, aimed at overcoming tensions that have impacted Turkey"s economy. Already-strained relations with Saudi Arabia collapsed after the killing by Saudi agents of journalist Jamal Khashoggi in the Saudi consulate in Istanbul. Turkey"s ties with Cairo have been poor since the military overthrew Egypt"s first democratically elected president, Mohamed Mursi of the Muslim Brotherhood. Erdogan, whose ruling AK Party is rooted in political Islam, had been a strong supporter of Mursi.