Moallem arrived Sunday in Iraq in the first such high-level visit by a Syrian official since the fall of Saddam Hussein's regime in 2003. He was expected to return to Damascus on Tuesday.
"Diplomatic relations will be restored between the two countries during the visit," Ali al-Dabbagh told The Associated Press.
The Syrians are plainly worried that escalating violence here could spill over their borders, along with a flood of Iraqi refugees, reports CBS News correspondent Elizabeth Palmer.
Iraq and the United States hope that Syria's offer of help means it will now get serious about choking off the flow of hundreds insurgent fighters who travel to Iraq over their common border.
Syria broke diplomatic ties with Iraq in 1982, accusing it of inciting riots by the banned Muslim Brotherhood in Syria. Damascus also sided with Iran in the 1980-88 Iran-Iraq war. Trade ties were restored in 1997.
Also Monday, four key lawmakers told the Associated Press that Iran has invited the Iraqi and Syrian presidents to Tehran for a weekend summit with Mahmoud Ahmadinejad to hash out ways to cooperate in curbing the runaway violence that has taken Iraq to the verge of civil war and threatens to spread through the region.
Iraqi President Jalal Talabani has accepted the invitation and will fly to the Iranian capital on Saturday, a close parliamentary associate said.
The Iranian diplomatic gambit appeared designed to upstage expected moves from Washington to include Syria and Iran in a wider regional effort to clamp off violence in Iraq, where more civilians have been killed in the first 20 days of November than in any other month since the AP began tracking the figure in April 2005.
The Iranian move was also a display of its increasingly muscular role in the Middle East, where it already has established deep influence over Syria and Lebanon.
"All three countries intend to hold a three-way summit among Iraq, Iran and Syria to discuss the security situation and the repercussions for stability of the region," said Ali al-Adeeb, a lawmaker of Prime Minister Nouri al-Maliki's Dawa Party and a close aide to the prime minister.
Both Iran and Syria are seen as key players in Iraq. Syria is widely believed to have done little to stop foreign fighters and al Qaeda in Iraq recruits from crossing its border to join Sunni insurgents in Iraq. It also has provided refuge for many top members of Saddam Hussein's former leadership and political corps, which is thought to have organized arms and funding for the insurgents. The Sunni insurgency, since it sprang to life in the late summer of 2003, has been responsible for the vast majority of U.S. deaths in Iraq.
Iran is deeply involved in training, funding and arming the two major Shiite militias in Iraq, where Tehran has deep historic ties to the current Shiite political leadership.
Many Iraqi Shiites spent years in Iranian exile during Saddam's decades in power in Baghdad. One militia, the Badr Brigade, was trained in Iran by the Revolutionary Guard.
An Ahmadinejad spokesman said that Talibani's visit was scheduled several weeks ago for late November to work on improving bilateral relations. But Majid Yazdi told The Associated Press that he had no information on a coming visit by the Syrian leader.
But Talabani confidants said the invitation was issued on Thursday by Iranian Ambassador Hassan Kazimi Qumi who said Syrian President Bashar Assad also would be in Tehran for the talks with Ahmadinejad.