The US is effectively "trapped" in Iraq, with the prospect of staying in the country as problematic as pulling out, the head of the UN has said.
A young boy was said to be among those who died in a US raid
Kofi Annan said the timing of a US withdrawal must be "optimal" so as not to create even greater chaos in Iraq.
He also urged Syria and Iran to assist efforts to stabilise their neighbour.
On Tuesday, Baghdad and Damascus resumed relations after more than 20 years, a move Iraq hopes will stem the flow of militants over the border.
Syria and Iran are now seen as positioning themselves for a future that could see a much-reduced US presence in Iraq.
Iran and Iraq have also arranged a summit in Tehran at the weekend, to which Syria has been invited. A proposal that Washington talk directly to Syria and Iran about helping to reduce the violence in Iraq is being widely discussed.
But while it is thought Washington is increasingly amenable to efforts at regional diplomacy, analysts say events may be moving faster than the US and the UK predicted or even wanted at this stage.
"The United States in a way is trapped in Iraq," Mr Annan said.
"It cannot stay and it cannot leave. There are those who maintain that its presence is a problem and there are those who say that if it leaves precipitously, the situation will get worse."
But there were calls again for a US withdrawal after three people - including a very young boy - were reportedly killed in a raid on a Shia militia stronghold.
Seven people were arrested, including the alleged leader of a militant group thought to be behind the kidnapping of a US soldier, the US military said.
"I am suspending my membership in Parliament since it remains silent about crimes such as this against the Iraqi people," said local Shia MP Saleh Al-Ukailli. "I will not return to parliament until the occupation troops leave the country."
Elsewhere in the country, at least 20 others died in insurgent attacks, including 10 people in the city of Baquba.
Announcing the accord with Syria, an Iraqi government spokesman said both sides had agreed US forces should stay in the country until they were no longer needed.
Relations between Syria and Iraq were severed in 1982, during Saddam Hussein's rule and soon after the beginning of the Iran-Iraq war.
"The latest talks between the Syrian and Iraqi side have been crowned by declaring a new era with the participation of the Syrian brothers in working on the security and stability with Iraq," the Iraqi foreign minister told the Associated Press news agency.
Hoshyar Zebari said the two sides had also agreed to cooperate on security issues.
White House National Security Council spokesman Gordon Johndroe said the US had always encouraged Iraq's neighbours to assist its government.
"Syria needs to now demonstrate that it is committed to constructive engagement and fostering an Iraq that can govern, sustain and defend itself," he said.