DUBAI - Iran and Saudi Arabia held their first foreign minister-level meeting since the 2013 election of President Hassan Rouhani, official Iranian media reported, signalling a possible thaw in chilly ties between the rival Gulf powers.Shi'ite Muslim Iran and the conservative Sunni kingdom have been engaged in a bitter contest for influence in the region, evident in political and military struggles in Syria, Iraq, Lebanon, Bahrain and Yemen.Foreign Minister Mohammad Javad Zarif suggested after his meeting in New York with his Saudi counterpart, Prince Saud al-Faisal, that the talks could lead to an improvement in relations."Both my Saudi counterpart and I believe that this meeting will be the first page of a new chapter in our two countries' relations," Iran's official IRNA news agency quoted Zarif as saying."We hope that this new chapter will be effective in establishing regional and global peace and security and will safeguard the interests of Muslim nations across the world."IRNA reported that Prince Saud, in a reference to the advance of Islamic State militants in Iraq and Syria, said he was aware of the sensitivity of the situation."We are aware of the importance and sensitivity of this crisis and the opportunity we have ahead of us. We believe that by using this precious opportunity and avoid the mistakes of the past, we can deal with this crisis successfully," he said."These two countries are influential in the region and cooperation between them will have clear effects on the establishment of regional and global security."The meeting takes place not long after Iranian Deputy Foreign Minister Hossein Amir Abdollahian made a state visit to Saudi Arabia in August, state news agency IRNA reported, in the first visit to Saudi Arabia by a senior government official since Iran's political landscape shifted in 2013.Hatred between Sunni Saudi Arabia and Shi'ite Iran, which has fueled a decade of violence across the region.In Syria, Iraq, Lebanon and Yemen, the two sides back sectarian proxy forces that are either at daggers drawn or openly at war in conflicts killing thousands each month.In Syria, each accuses the other of responsibility for a bloodbath, with Iran supporting President Bashar Assad and Saudi Arabia funding the rebels trying to overthrow him. In Iraq, sectarian violence is at its worst since 2008.Riyadh accuses Tehran of fomenting trouble in Bahrain and even Saudi Arabia itself. Tehran accuses Riyadh of plotting its destruction with Washington.