The Obama administration has found itself in a foreign policy and national security pickle of rare complexity with the apparent entry of Syria into the Iraq conflict on the side of the US-backed government in Baghdad, as well as active Iranian military support for Iraqi Prime Minister Nouri al-Maliki.

Washington already was toeing a delicate line with Shiite Iran, which the US deems the world's most active state sponsor of terrorism, over their common short-term interest in turning back the advance of militant Sunni rebels in Iraq.

Now, to its dismay, Syrian President Bashar Assad — regarded in Washington as a pariah who should be ousted — has joined the club with what US and Iraqi officials say are airstrikes against the Islamic State of Iraq and the Levant in western Iraq. ISIL had been fighting Assad in Syria before turning its major focus to seizing large swaths of northern Iraq.

Assad is being supported by Iran in his country's own civil war with opposition forces, and a decision for Syria to hit ISIL on Iraqi soil is perhaps not surprising. While al-Maliki may not like Syrian attacks on Iraqi territory, if it distracts the Islamic State from its trek toward Baghdad for a while, then they will welcome it.

But as Iraq's other immediate neighbours — Jordan, Kuwait, Saudi Arabia and Turkey — bolster their defences, the new fighting threatens to unravel a byzantine balance of Mideast alliances and enmities that the United States long has sought to manage. The US is deploying 300 special forces to train and advise the Iraqi army and is conducting surveillance flights. Iran is also flying surveillance drones over Iraq in aid of al-Maliki's government, and on Tuesday, Syrian planes killed 17 people in a strike in Iraq's mainly Sunni Anbar province, according to US and Iraqi officials.

American and Iranian officials have had some direct discussions on the matter, though the administration has ruled out the prospect of direct military cooperation or coordination with Iran.

However, amid widespread concern, notably among Sunni Arab states and Israel, about the convergence of US, Iranian and Syrian policies on ISIL, President Barack Obama's national security team has scrambled to produce a consistent and coherent message to the region. Administration officials said intervention by Syria was not the way to stem the insurgents, who have taken control of several cities in northern and western Iraq.

Obama and his top aides have said repeatedly that the only way to resolve the crisis is for Iraqi leaders to come together and form a truly inclusive and representative government in which all three of the country's main ethnic and religious groups — Sunni, Shiite and Kurd — have a voice.

Yet, it remains unclear if al-Maliki is willing to allow such an administration to be formed, and as long as the crisis continues, Gulf Arab countries with their long and deep distrust of Iran in particular are watching Iraq with increasingly dire concern.

At the White House, spokesman Josh Earnest blamed Assad for the rise of the extremists and warned that Syrian intervention could make matters worse.

"The solution to the threat confronting Iraq is not the intervention of the Assad regime," he told reporters. "In fact, it's the Assad regime and the terrible violence that they perpetrated against their own people that allowed ISIL to thrive in the first place. The solution to Iraq's security challenge does not involve militias or the murderous Assad regime, but the strengthening of the Iraqi security forces to combat threats."

Karim Sadjipour, an Iran expert with the Carnegie Endowment for International Peace, said the situation in Iraq, coupled with ongoing US-Iran nuclear negotiations, have produced a "bizarre dynamic" in which the United States and Saudi Arabia appear to be "allies but not friends" and the United States and Iran appear to be "friends but not allies."

The addition to the mix of Syria's Assad is likely to further muddy the waters.