In a bid to get lasting security, Iraq has invited its neighbours and representatives of the UN Security Council permanent members to meet in Baghdad on Saturday.
The gathering is expected to include Iran and Syria, as well as the United States and Britain.
Last year S
yria and Iraq resumed diplomatic relations that were severed more than 25 years ago over ideological disputes and Syria's support of Iran in its 1980-88 war with Iraq.
American and Iraqi officials have repeatedly accused Damascus of not doing enough to stop insurgents from crossing the border into Iraq to fight US and Iraqi troops, a charge Syria denies.
Hashemi, who also met Bashar Assad, Syria's president, during the visit, said he discussed the "role Syria could play" in promoting stability in Iraq.
"We came up with joint visions and analysis of the situation and the way to deal with the situation in Iraq," said al-Hashemi, without providing details.
Asked if Syria expected a direct dialogue with the US at the Baghdad conference, al-Sharaa said the gathering was not focused on that issue.
"The aim of the Iraq conference is to help Iraq and the Iraqi people. We hope to open a horizon in solving this big problem and Syria will do its best to help Iraq succeed in the national reconciliation process," he said.
Al-Hashemi said he had expressed Iraq's concerns over Iran's role in Iraq, adding he would also relay those concerns to Iranian officials when he visits Tehran next week.