Prime Minister Haider al-Abadi of Iraq and Prime Minister Ahmet Davutoglu of Turkey meet in Teheran.   In the Iraqi capital, from shopping malls to fancy hotels to the shelves of grocery stores, the influence of Turkish business is ample, underscoring an economic relationship between Turkey and Iraq has flourished even as the diplomatic relationship has soured in recent years.

Now, with the new Iraqi government struggling to keep the country together while under attack from Islamic State militants, and with Turkey dialing back its ambitions of leading a Sunni political axis that would reshape the region, the two countries are trying to come together amid mutual suspicion.

The visit by Prime Minister Ahmet Davutoglu, the first from a Turkish prime minister in nearly four years, was a vivid example of a scramble taking place all across the Middle East, as former adversaries are seeking to mend relationships, or at least try to work together, at a time of unprecedented crisis.

Mr. Davutoglu’s visit on Thursday came a week after a tentative agreement between Baghdad and officials in Erbil, the Kurdish capital, that restarted budget payments to the Kurds and allowed the Kurds to export some of their own oil.