By Orhan Coskun and Gulsen Solaker ANKARA (Reuters) – Prime Minister Tayyip Erdogan will be banking on Kurdish support if he bids for Turkey’s presidency in an August election and is likely to use his party’s strong showing in local polls as a mandate to advance peace talks with Kurdish militants. Erdogan’s AK Party emerged well ahead of rivals in municipal elections on Sunday, increasing its share of the vote including in parts of the Kurdish-dominated southeast. The outcome has bolstered his hand in a peace process in which he has invested much political capital despite staunch nationalist opposition. Erdogan has made no secret of his desire to run for Turkey’s first directly-elected presidency in four months’ time.