"I hope Iran and Turkey would experience closer and friendlier ties and expand their cooperation for settlement of regional crisis," President Rouhani said during a phone conversation with Erdogan on Monday.
He further congratulated Erdogan over his new post.
The Iranian president stressed the need for both countries to boost cooperation in settlement of disputes in Iraq, Syria and Palestine, and said, "Combating terrorism in the region, specially Iraq is one of the necessities for cooperation between the two countries."
President Rouhani voiced his concern over the ongoing bloodshed in Iraq, and said, "A legal government must be formed in that country as soon as possible."
Erdogan, for his part, called for enhanced relations with Tehran, and voiced his country's enthusiasm for coordinating efforts over ending bloodshed in Iraq, Syria, and Gaza.
Erdogan secured 51.96 percent of the vote on Sunday, making a run-off unnecessary.
Turkish prime minister has been elected by absolute majority vote to a five-year term as president, making a second round scheduled for August 24 unnecessary.