An opinion poll suggests most Iraqis feel their lives have improved since the war in Iraq began about a year ago.
A lack of jobs is one of the most immediate problems in Iraq
The survey, carried out for the BBC and other broadcasters, also suggests many are optimistic about the next 12 months and opposed to violence.
But of the 2,500 people questioned, 85% said the restoration of public security must be a major priority.
Opinion was split about who should be responsible, with an Iraqi government scoring highest.
Creating job opportunities was rated more likely to improve security effectively than hiring more police.
However on various issues, there were stark differences of opinion according to region or ethnic group.
About 6,000 interviews were carried out in total, half in Autumn last year and half this Spring, in a project run by Oxford Research International.
Seventy per cent of people said that things were going well or quite well in their lives, while only 29% felt things were bad.
And 56% said that things were better now than they were before the war.
Th poll company's director Dr Christoph Sahm, said Iraqis trained as interviewers travelled around the country to speak to randomly selected people in their homes.
The survey reflected Iraq's distribution of population, balance between men and women, and religious and ethnic mix.
Dr Sahm said: "I would call it very extensive; It is a national survey and it is also representative... the key finding is that Iraqis don't want to break up the country."
Meanwhile, an ICM poll of British attitudes about the Iraq war for BBC Newsnight's special programme, One Year On - Iraq, reveals that 48% of those questioned thought taking military action was the right thing to do; 43% thought it was not.
There is an almost even split on whether the war was legal, while 34% of interviewees believe the war has contributed to the security of the UK against 55% who believe it has not.
US 'will take heart'
In the poll of Iraqis, nearly 80% favoured a unified state with a central government in Baghdad; only 14% opted for a system of regional governments combined with a federal authority.
The majority was even bigger among Iraqi Arabs, but for the Kurdish minority, the situation was reversed, with more than 70% backing a federal system.
There is an existing Kurdish regional government in the north, the powers of which were recognised by Iraq's interim constitution, signed last week.
BBC diplomatic correspondent Barnaby Mason says the American and British governments will take some comfort from the results.
The survey shows overwhelming disapproval of political violence, especially of attacks on the Iraqi police but also on American and other coalition forces.
But among Arabs, nearly one in five told the pollsters that attacks on coalition forces were acceptable.
About 15% say foreign forces should leave Iraq now, but many more say they should stay until an Iraqi government is in place or security is restored.
Looking back, more Iraqis think the invasion was right than wrong, although 41% felt that the invasion "humiliated Iraq".
But by ethnicity, only one in three Arabs believed their country was liberated - compared to four out of five Kurds.
Dan Plesch, a security expert at Birkbeck college in London said that the poll was good news for the leaders of countries who began the invasion a year ago this week.
"This poll indicates that Iraqis strongly support a unified country with strong leadership. They don't want to see the country divided up and they don't want to see an Islamic government."
Regaining security is rated as by far the highest priority at 85%, followed by holding elections for a national government (30%), ensuring the majority of Iraqis can make a decent living (30%) and reviving the economy (28%).
And only just over a third of people report that their electricity supply is good.
A key concern for the Americans as they prepare to hand over power in June is the unpopularity of the people they are putting in place.
Their favoured son Ahmed Chalabi had no support at all, while Saddam Hussein remains one of the six most popular politicians in the country.
Dr Mustafa Alani of the Royal United Services Institute said that the Iraqis wanted a strong leader, but had not found one yet.
"The main point is that the Iraqis are now looking for a strong leader who can save the day.
"As long as the governing council is considered illegitimate and illegal in Iraq, I think they will have to work hard to find something more legitimate and more legal before they disengage from the country."
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