"We've always encouraged Iraq's neighbours to take a role in supporting and assisting the unity government in Iraq," Gordon Johndroe, spokesman for the White House's national security council, told AFP.
"Syria needs to now demonstrate that it is committed to constructive engagement and fostering an Iraq that can govern, sustain and defend itself," Johndroe said.
"One of the first steps Syria could take is to strengthen it's border with Iraq and stop the flow of foreign fighters into that country," he said.
Iraqi Foreign Minister Hoshyar Zebari, at a joint news conference with his visiting Syrian counterpart Walid Muallem, announced Tuesday that Iraq was restoring full diplomatic relations with Syria after a 26-year break.
Zebari also said the neighbours agreed on closer security co-operation following repeated US accusations that Syria was turning a blind eye to Sunni Arab insurgents smuggling men and materiel across the border.
Muallem said he hoped the restoration of normal relations would put an end to US criticism of Syria over its role in Iraq. "I do not want to go back to the former accusations. We seek future co-operation in all fields," he said.
Although Iraqi officials have visited Damascus, Muallem, who arrived Sunday, was the first Syrian official to visit Baghdad since the US-led invasion of 2003.
Saddam Hussein's regime cut ties with Syria in 1980 in protest at its support for Iran after an eight-year war between the two neighbours broke out that year.
The rapprochement between the two neighbours comes amid mounting calls for the US administration to engage Syria and its regional ally Iran in efforts to stabilise Iraq three and a half years after the invasion.
Muallem's trip followed a string of appeals from Syrian officials for renewed talks with the United States.
This has been echoed by a growing chorus of demands in Washington for Bush to drop his policy of isolating Syria and Iran, a drumbeat that has intensified since the Democrats won control of Congress this month.
Senator Joseph Biden, who will chair the powerful Senate Foreign Relations Committee when the Democrats take over in January, called Monday for talks to bring Syria and Iran into a "non-aggression agreement" with the Iraqi regime.
Former secretary of state Henry Kissinger, an influential adviser to Bush on Iraq, added his endorsement to the idea at the weekend.
Engagement with Syria and Iran is expected to be a key recommendation the Iraq Study Group, a bipartisan panel chaired by former Republican secretary of state James Baker, will present to the White House early next month.
Scott Lasensky of the US Institute for Peace, a think tank that is advising the Baker panel, said Muallem's visit to Baghdad amounted to a "vote of confidence" in the embattled Maliki government.
"There are some elements of the visit that will both energise and give more weight to the (policy) review here and the argument to engage the Syrians," he said.
The Bush administration, which withdrew its ambassador from Syria last year over suspected Syrian involvement in the assassination of former Lebanese prime minister Rafiq Hariri, has so far strongly resisted the pressure.
"There's no indication that Syria wishes to be a stabilising force," Secretary of State Condoleezza Rice said last week, pointing to Syrian meddling in Lebanon, its role in Iraq and its support for radical Palestinian factions.
"That's not a very good record on which to suggest that just going and talking to Syria is going to get a change in their behaviour," she said.
Bush arrived in the US island state of Hawaii Monday after wrapping up a week-long trip to Asia.

Copyright AFP (Agence France-Presse), 2006