The meeting between the two parties on Saturday came two days after Iraqi Prime Minister Nuri al-Maliki announced that his country would put forward a peace initiative to Syria.
"America and Europe are afraid of the phase after Bashar al-Assad. That is why they understand the [our] initiative,” Maliki said.
Fayadh is now scheduled to travel to the Egyptian capital of Cairo, where his team will present the results of their meeting with Syria to the Arab League (AL).
The AL on November 12 voted to suspend Syria until after a peace plan proposed by the body and accepted by Damascus on November 2, 2011, has been implemented by the Syrian government.
Moreover, the AL also approved unprecedented sanctions against Syria, including cutting transactions with the Syrian Central Bank and placing an embargo on investment projects in the country.
Iraq, however, abstained from both the vote to suspend Syria from the Arab body as well as placing sanctions on Damascus.
Iraqi officials fear that instability in Syria could spill over the border.
Syria has been experiencing unrest since mid-March, with demonstrations being held both against and in favor of President Assad. Hundreds of people, including members of the security forces, have been killed in the turmoil.
While the opposition and Western countries accuse Syrian security forces of being behind the killings, Damascus blames outlaws, saboteurs and armed terrorist groups for the deadly violence, stressing that the unrest is being orchestrated from abroad.
Syrian opposition groups have also been interviewing Israeli news outlets over the past few months. The interviews clearly show the opposition's vision for the future of Syria, and indicate their interest in developing relations with Tel Aviv.
Meanwhile, the confession of Syrian rebels to carry out armed activities and killing people as well as security forces proves that recent developments in the country are to be seen as parts of an attempt to start a revolt in order to overthrow the current government and replace it with a US-backed regime.