Turkish Prime Minister Recep Tayyip Erdogan is in Baghdad for talks with Iraqi leaders.
Discussions are expected to focus on security issues and efforts to tackle the Kurdish rebel group, the PKK.
Mr Erdogan is also expected to sign trade agreements and discuss Iraqi investment and reconstruction plans.
He is only the second leader of a country neighbouring Iraq to visit the country since the US-led invasion to overthrow Saddam Hussein in 2003.
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King Abdullah of Jordan had been expected to visit earlier this week, but the trip was called off at the last minute over security concerns.
Cross-border attacks
The main issue between Iraq and Turkey is the presence in the mountainous northern Iraqi border region of fighters from the rebel Turkish Kurdish movement, the PKK.
They have been blamed by Ankara for a number of cross-border attacks.
Turkey has launched ground, air and artillery attacks on suspected PKK bases in northern Iraq, which is generally under the control of the Iraqi Kurdish regional government and its forces.
The BBC's Jim Muir in Baghdad says that for the Iraqi government, the vital thing is the visit itself.
The visit by Mr Ahmadinejad reinforced the perception that Iraq, under its new government dominated by Shia Muslims and Kurds, was falling under Iranian influence.
The Iraqi government is keen to counter that impression, by encouraging closer ties with other regional states. Turkey has been the first to respond.
Other mainly Sunni Arab states have plans to revive their embassies and involvement in Baghdad, but it's proving a slow process.
(BBC)
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