In December, the countries reopened their embassies in each other's capitals.
Talabani, speaking at the public meeting with the Syrian leader soon after his arrival, said: "Syria stood with us in difficult times. I came here with a large delegation to show our seriousness about advancing our relations with Syria."
Talabani, a Kurd, founded the Patriotic Union of Kurdistan in the 1970s, when he, along with other exiled opponents of Iraq's Baathist government, was living in Syria.
On Friday, an official from Talabani's office said the Iraqi president and al-Assad are expected to sign a number of agreements related to bilateral security and commercial matters.
|"The enmity between the United States and Syria and Iran doesn't benefit the situation in Iraq"|
Mahmoud Othman, Iraqi politician
US and Iraqi officials have repeatedly accused of Syria of failing to prevent Sunni fighters from entering Iraq.
Syria denies the charge and says that the Iraqis and US forces are not doing enough to guard their side of the border.
When outlining a new strategy for Iraq on Wednesday, Bush vowed military action to disrupt supplies of weapons coming into Iraq from Syria and Iran.
"The timing may seem a little tricky after what Bush said," Mahmoud Othman, a prominent Iraqi politician with close ties to Talabani, told the Associated Press.
"But our interests differ from those of the United States. The enmity between the United States and Syria and Iran doesn't benefit the situation in Iraq."
Visit planned a year in advance
"[Bush's plan] very much puts Iraqis at the centre of responsibility"
Condoleezza Rice, US secretary of state
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The visit has been planned for nearly a year and its date was finalised about two weeks ago, he said.
Engaging with Iraq could offer Assad's government an opportunity to ease its relative isolation in the region.
"Syria can play a constructive role in Iraq, but not necessarily a decisive one," Rami Khouri, a Beirut-based Middle East expert, told The Associated Press.
"What Syria can and cannot do will not decide the future of Iraq, but it can help."