* Turkish foreign minister visits disputed city
* Baghdad says its constitution has been violated
* Neighbours at odds since end of last year
By Barry Malone
BAGHDAD, Aug 3 (Reuters) - Iraq made a formal protest to Turkey's envoy in Baghdad on Friday after the Turkish foreign minister made a surprise visit to an oil-rich Iraqi city claimed by both the central government and the country's autonomous Kurdistan region.
The episode, the latest in a series of diplomatic spats and tit-for-tat summonings of envoys between the neighbouring countries, is likely to worsen already strained relations.
Turkish Foreign Minister Ahmet Davutoglu had travelled to Kirkuk on Thursday after visiting the regional president in Arbil, the capital of Iraqi Kurdistan.
But Iraq's foreign ministry accused Turkey of violating its constitution with the visit, saying that Davutoglu had neither asked for nor obtained permission to enter Kirkuk.
A junior minister at Iraq's foreign ministry had handed Turkey's charge d'affaires a protest letter on Friday, a strongly-worded statement from the foreign ministry said.
"The note also included a demand by the Iraqi government (for an) urgent explanation from the Turkish government," it added.
Relations between Iraq, close to Shi'ite Iran, and Sunni Muslim regional power Turkey, were tested after U.S. troops pulled out of Iraq last year and the government immediately tried to arrest one of its Sunni vice presidents.
He fled first to Kurdistan and later to Ankara, where he was given refuge.
Iraqi Prime Minister Nuri al-Maliki and Turkey's Prime Minister Tayyip Erdogan then traded public insults.
Baghdad's Arab-led central government and ethnic Kurdish officials are locked in a protracted dispute over who controls territory and oilfields along their internal border. Kirkuk, which possesses huge crude oil reserves, is one of those areas.
Iraq and Turkey are also at odds over the worsening conflict in Syria. Turkey has become one of the main backers of the rebels, while Baghdad has refused to support calls for President Bashar al-Assad to step aside.
Iraq is Turkey's second largest trading partner after Germany with trade reaching $12 billion last year, more than half of which was with the Kurdish region. (Editing by Andrew Osborn)