By Michelle Moghtader DUBAI (Reuters) - Iran's deputy foreign minister said he held "positive and constructive" talks with Saudi Arabia's foreign minister on Tuesday where Islamist militancy in Iraq - that both see as a threat - was one of the topics discussed. Hossein Amir Abdollahian was in Jeddah for the first high-level bilateral talks between the two countries since Hassan Rouhani was elected president of Iran a year ago, pledging to thaw Tehran's frosty relations with its Arab neighbors. "Both sides emphasized the need to open a new page of political relations between the two countries," Abdollahian told Reuters by telephone after meeting Prince Saud al-Faisal. The two men discussed issues of regional security such as the rise of the Islamic State militant group in Iraq and Israeli attacks on Gaza, Abdollahian said, adding: "The meeting took place in a very positive and constructive atmosphere." Official Saudi media did not initially report on Abdollahian's arrival, a sign of the sensitivity of relations between two of the Middle East's big powers which are separated by the Gulf and a religious divide, with Sunni Muslim Saudi Arabia often at odds with Shi'ite Iran.