Allawi, whom opponents have accused of leaning on the support of Iran's regional rival Saudi Arabia in the drawn out coalition talks that have left Iraq without a government since an inconclusive March 7 general election, said that it was Iran that was blocking progress in the talks.
"We have been asking leaders who have good relations with Iran to ask it not to interfere in Iraqi affairs and we discussed this with President Assad," Allawi said.
Assad, who is to make a state visit to Iran soon, "promised to make every effort for Iraq and the region's stability," he added.
Allawi's Iraqiya bloc, a broadly secular grouping which drew most of its support from Sunni Arab areas, won 91 of the 325 seats in parliament in the March election, two more than Maliki's State of Law Alliance, a Shiite grouping.
Neither came close to winning an overall majority, and no new government has been formed since, although Allawi insists his grouping should have the first opportunity to try to form a government.
In a statement released late on Friday, Allawi's bloc ruled out taking part in any new coalition led by the incumbent prime minister.
"Iraqiya believes the current type of government headed by Maliki cannot be repeated, so Iraqiya will not take part in any government headed by him," it said.
Allawi's bloc has repeatedly accused Shiite Iran of meddling in the coalition talks to block his candidacy for the premiership.
Maliki's supporters in turn accuse Saudi Arabia of refusing to abandon its efforts to promote Allawi's candidacy.
Allawi insisted on Wednesday that his bloc was not inimical to Iranian interests, even though its support is mainly Sunni.
"Iraqiya is not hostile to Iranian policy and we believe that we have genuine common interests but we absolutely reject any interference in Iraqi affairs," Allawi said.
In its report of the meeting, the official Syrian Arab News Agency made no mention of any request by Allawi for representations to Iran.
Assad told Allawi that Syria would "support any agreement that gets Iraqis out of the current crisis and contribute to the formation of a government of national unity that brings together all the forces represented in parliament," SANA said.
Allawi spoke of the "enormous confidence Iraqis have in Syria which has kept itself at an equal distance from all Iraqi parties," the news agency added.
It was Allawi's second meeting with Assad in recent months. The two met in July, when Allawi also held talks with Shiite radical leader Moqtada Sadr as part of his efforts to form a majority.
The standoff between Allawi and Maliki over the premiership has dragged on for months, sparking growing concern in Washington.
"The vice president urged Dr Allawi, as he is urging all Iraqi leaders, to expedite efforts to form an inclusive and legitimate government responsive to the needs of the Iraqi people," Biden's office said.
Source: AFP Global Edition