Al-Jaafari met Arinc on Saturday before departing from Ankara. Arinc was standing in for President Ahmet Necdet Sezer, who was visiting Bulgaria.
At the Ankara airport, just before departing, al-Jaafari was asked whether his new government had a timetable for the withdrawal of US forces in Iraq.
Al-Jaafari said a withdrawal can only take place after Iraqi security forces were fully in place.
"After a security force has been fully established we can ask for a withdrawal of the multinational force," he said, but indicated that could take a long time.
Iraq, he said, was going through a "sensitive period".
Al-Jaafari, on his first foreign visit since taking office, met Prime Minister Recep Tayyip Erdogan and other officials on Friday, and pledged to prevent Turkish Kurdish rebels based in Iraq from carrying out cross-border attacks.
Turkey is insisting that Iraq and the United States crack down on the rebels, who for more than a decade have been able to take advantage of instability in the north to run their campaign against Turkey.
"On the basis of good neighbourly relations, we will not allow any group to harm any neighbouring country"
Iraqi Prime Minister
"On the basis of good neighbourly relations, we will not allow any group to harm any neighbouring country," al-Jaafari said.
But despite the statement, Iraqi security forces are barely able to keep control within Iraq and there is little indication that US or Iraqi forces are willing now to fight the Turkish Kurdish rebels.
Meanwhile, Turkish Trade Minister Kursad Tuzmen on Saturday said trade volume between the two countries could reach $2.5 billion by the year end.