Some experts believe that the US troops' surge and accompanying Iraqi government crackdown on the militias is the last chance to stabilise the country.
There have been warnings that the crisis could spread to the rest of the region.
BBC News website's world affairs correspondent, Paul Reynolds, examines what is at stake for Iraq's neighbours.
Turkey has three main interests in the stability and unity of Iraq. It opposes the emergence of a separate Kurdish state in the north along its border, because that might encourage Kurdish nationalism among its own Kurdish population. It wants an Iraq stable and strong enough to clamp down on the Kurdish PKK rebels who have set up bases in Northern Iraq.
Turkey has a secular state and mainly Muslim population
It also opposes an Islamic state in Iraq because that might undermine its own model of being a secular state with a Muslim population.
It is therefore supporting the US effort in Iraq, which it sees as the most likely way to achieve its goals.
However, co-operation with the United States is sometimes fragile. Turkey refused to allow the US 4th Division to invade Iraq from its territory in 2003 and is currently concerned about a resolution in the House of Representatives in Washington which calls on the US government to recognise the mass killing of Armenians from 1915 as "genocide".
The Bush administration opposes the resolution while accepting that "mass murder" and "ethnic cleansing" took place. It does not want to jeopardise relations with Turkey, which it is trying to develop. US Assistant Secretary of State Daniel Fried told a House committee on 15 March that 74% of US air cargo into Iraq goes through the Turkish base at Incirlik. Much of the fuel used by US forces in Iraq and fuel and food for Iraqis as well goes across the land border.
Iran is the neighbour that has perhaps emerged strongest from the US-led invasion of Iraq in 2003. The invasion ended any military threat from Iraq by ending the rule and later the life of the man who launched a war against Iran that lasted from 1980 to 1988. Iran's fellow religionists, Shia Muslims, dominate the current government of Iraq with the Sciri party, which has close links to Iran, playing a leading role.
Iran is accused of supporting Shia militias in Iraq
In November 2006, Iran and Syria announced that they were restoring diplomatic relations with Iraq. With the US, both attended a regional conference in March this year called by the Iraqi government to try to encourage support for Iraq. However, Iran's role in Iraq has been criticised by the US and UK which accuse it of supporting Shia militias, especially the Mehdi army, that have attacked American and British forces, a claim Iran denies. Iran in turn says that the main source of instability in Iraq is the presence of foreign troops.
Iran is not thought to be interested in a break-up of Iraq. Ideally its leadership might prefer an overtly Islamist government in Iraq, but in any event it would like to see the Shia-led government gain full control of the country. In that way, its relations with its neighbours would be secure.
The issue of Iran's nuclear programme is a sensitive one, with the US leading the effort to extend UN sanctions on Iran and Iraq sitting uncomfortably in the middle.
Syria has adopted an uncertain policy towards Iraq since the invasion of 2003. On the one hand it was pleased at the demise of Saddam Hussein.
It sided with Iran during the Iran-Iraq war because of disagreements between Saddam Hussein and the then Syria leader President al-Assad, father of the current president. Syria even sent troops to fight in the 1991 war to remove Iraq from Kuwait.
Syria and Iraq resumed diplomatic relations in 2006
On the other hand it is concerned about the presence of US troops next door and at the hostile policy of the Bush administration. President Bush once described Syria as part of an "axis of evil". The US has accused it of allowing Sunni Islamic fighters to cross its border to take part in the insurgency.
However, last November it joined with Iran in restoring diplomatic relations with Iraq and, with Iran and the US, attended a regional conference in March organised by the Iraqi government.
It thereby signalled its interest in stabilising Iraq, perhaps believing that the quickest way to get US troops out would be for the Iraqi government to gain control. This appears to be part of its desire to develop better relations with the rest of the Arab world, especially Saudi Arabia, with whom it fell out over particularly its role in Lebanon. It was pleased to be invited to a regional summit in the Saudi capital Riyadh at the end of March.
Jordan has followed its traditional path of trying to balance its own interests between sometimes competing pressures. It wants to maintain good relations with the United States but at the same time has had to find a way of developing relations with the new government of Iraq which is no longer dominated by the Sunni interests with which Jordan previously had close ties. Jordan's King Abdullah comes from the Hashemite royal family, which provided Iraq's first king, Faisal.
Jordan's King Abdullah II wants to maintain relations with the US
Jordan was also an ally of Saddam Hussein during the Iran-Iraq war and initially supported Iraq after its invasion of Kuwait. However, following the invasion of Iraq in 2003, a bomb attack on Jordanian embassy in Baghdad in August that year, in which 19 people were killed, was an early indication that the insurgents saw Jordan as an enemy.
So Jordan made its peace with the Iraqi government and sent its prime minister on a visit to Baghdad in September 2005, the first by an Arab leader since the fall of Saddam Hussein.
Jordan accepts that any Iraqi government will be dominated by the majority Shia but wants a strong Sunni presence.
It also has an interest in stopping Iraq from disintegration, for fear that the already high number of refugees going to Jordan will increase substantially.
Saudi Arabia opposed the war against Iraq in 2003 and has recently become concerned at the growth of Iranian and Shia influence, which it thinks is partly the result of that invasion. So it has embarked on a diplomatic effort to rally Arab governments in an alliance to counter that influence.
It is especially worried about the prospect of Iran developing a nuclear bomb, something Iran denies it intends to do.
Saudi Arabia has suffered alleged al-Qaeda attacks on its own soil
The Saudi government wants a broadly based government to develop control in Iraq, one that includes representative Sunnis. However, some elements within Saudi society are thought to be sympathetic to the Sunni insurgents and the Iraq Study group led by the former US Secretary of State James Baker concluded that some rich Saudis had sent money to the insurgents to buy weapons. This has been an embarrassment to the Saudi government because it needs to keep in with the United States.
Its public opposition to the invasion has been quietly followed by practical acts of help, especially on the intelligence front. The Saudis and the Americans have a common interest in opposing al-Qaeda resistance, from which Saudi Arabia has suffered on its own soil.
Its heightened role has also been seen in its diplomacy surrounding the Israeli-Palestinian dispute. It brokered a deal between Hamas and Fatah for a new Palestinian government and proposed a revived peace plan first agreed in Beirut in 2002.
Kuwait supported the US invasion of Iraq in 2003, which was launched from its territory. US and other foreign forces have been partly sustained from Kuwait ever since. Kuwait's motivation was hostility to Saddam Hussein who invaded Kuwait in 1990 despite its support for him during the Iran-Iraq war.
Kuwait's hostility towards Saddam Hussein remained long after Iraq's 1990 invasion
Having got rid of their main enemy, the Kuwait rulers now desperately want the wider US aims in Iraq to work. Like Saudi Arabia and other Arab states, Kuwait would like to see a unified Iraq with good Sunni representation. It, too, is concerned about the rise of Iran.
However President Mahmoud Ahmadinejad visited Kuwait in February 2006 to try to improve relations, the first visit there by an Iranian leader for 27 years.
Iran said diplomatically that Kuwait has been "misled" by Saddam Hussein. Kuwait also hopes that a future, strong and stable Iraqi government will finally end talk in Iraq that Kuwait, with its oil riches, is simply a lost Iraqi province.