Erdoğan infuriated Iranians last month when he said the Islamic republic was “trying to dominate the region” and accused Tehran of pursuing a sectarian agenda in Syria, Iraq and Yemen. More than 60 Iranian MPs had asked for his visit to be cancelled.

Despite this, Erdoğan was welcomed by Rouhani in the Iranian capital on Tuesday and, in an unusual departure from Tehran’s diplomatic protocol, the Turkish leader’s motorcade had a mounted escort as it made its way into the Saadabad palace, following a similar ceremony held for the Iranian president in Ankara.

Erdoğan also met Ayatollah Ali Khamenei, the supreme leader in Iran. In a direct reference to Turkey’s support for the Saudi-led intervention there, Khamenei’s Twitter account announced later: “Solution to Yemen crisis is to stop foreign intervention & invasion. It’s on Yemenis to decide for their future.”

“We’ve had a substantial and good meeting,” Rouhani said in a joint press conference after the two leaders met behind closed doors, praising Turkey for welcoming the preliminary agreement reached in high-level nuclear negotiations in Switzerland.

“Our both countries want to increase the [bilateral] trade volume from $14bn [£9.5bn] in the previous year to nearly $30bn,” the Iranian president said. Rouhani predicted that a final agreement between Iran and the west, which could lead to the lifting of economic sanctions, would boost economic ties between Tehran and Ankara.

Turkey imported almost $10bn worth of goods from Iran in 2014 and exported a total of $4bn. Ankara provided a financial lifeline to Tehran when international sanctions cut off its banking system from the outside world by paying for Iranian natural gas in gold.

Iran and Turkey share a long border and have had peaceful relations in modern times, usually putting economic relations over regional politics. But relations became frosty as the two capitals followed opposing paths over the Syrian conflict.

Iran has extended unwavering support for Bashar al-Assad’s regime, while Turkey backed Syrian opposition forces and called for Assad to be removed from power. In Yemen, too, they have strong disagreements: Iran supports the Shia Houthi rebels but Turkey has backed Saudi Arabia’s air strikes against the Houthi forces, also known as Ansar Allah (the Supporters of God). In recent months, Turkey has become closer to Iran’s main rival in the region, Saudi Arabia.

Erdoğan sparked a row in March after voicing opposition to Iran’s growing influence in the Middle East, echoing similar concerns made by Saudi Arabia and other Gulf states. He urged Tehran to respect the territorial integrity of Syria, Iraq and Yemen by withdrawing any forces it has in those countries.

“Iran’s attitude towards the matter is not sincere because they have a sectarian agenda. So they will want to fill the void that will be created by Daesh [Islamic State] themselves,” Erdoğan said at the time.

Iran’s foreign minister, Mohammad Javad Zarif, strongly objected. “It would be better if those who have created irreparable damages with their strategic mistakes and lofty politics would adopt responsible policies,” he said.

Iran accuses Turkey of supporting takfiris, its terminology for Sunni extremists. Hossein Shariatmadari, the hardline editor of the state-run newspaper Kayhan, said before Erdoğan’s arrival that the Turkish president’s visit to Tehran was an insult to the Iranian people.

Fadi Hakura, an expert on Turkey and associate fellow at Chatham House, said it was unlikely that such disputes would lead to a complete breakdown in relations between the two states. “Iran and Turkey have maintained their bilateral relationship in the face of major disagreements over regional issues. They cannot afford to allow their bilateral relations to experience a complete rupture.

“The two countries share a common border, which is the most peaceful border in the Middle East since the 17th century, and they have substantial energy and economic ties.”

Nevertheless, Hakura said relations were not as warm as they had been five years ago. “Iran no longer trusts Turkey as an effective mediator and does not engage in strategic dialogues with Turkey on the nuclear issue or other issues such as Iraq, Syria and Yemen,” he said.

“In essence, the Arab spring has brought the so-called Sunni/Shia divide to the surface and that has led to the cooling of relations between Tehran and Ankara.”

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