By Jonathan Marcus
BBC diplomatic correspondent
Click below to see the poll's key results in graphs
More details
That is a question more for military analysts and security experts.
But if the findings of a new opinion poll for the BBC are anything to go by, it certainly seems to be losing the battle for global public opinion.
The poll was carried out by the international opinion research firm GlobeScan, together with the Programme On International Policy Attitudes at the University of Maryland (Pipa) in the US.
"Though the Bush administration has framed the intervention in Iraq as a means of fighting terrorism, all around the world - including in the US - most people view it as having increased the likelihood of terrorist attacks," Pipa director Steven Kull notes.
"The near-unanimity of this assessment among countries is remarkable in global public opinion polling."
Staying put?
The poll also indicates that there is a strong body of opinion in 20 of the 35 countries surveyed that believes US-led forces should withdraw from Iraq in the next few months.
POLL: VIEWS ABOUT IRAQ Poll results in detail (2.6MB) Most computers will open PDF documents automatically, but you may need to download Adobe Acrobat Reader. Download the reader here
In Iraq itself, opinion is evenly divided with 49% favouring an early withdrawal and the same number wanting US-led forces to stay.
However, in terms of global opinion, the picture changes sharply if the Iraqi government asks the troops to stay.
In this case, there are majorities for the troops remaining until the job is done in two-thirds of the countries questioned.
That scenario did not change too many people's minds in Saudi Arabia, Egypt, and Turkey, where there were still clear majorities for the US troops to leave as soon as possible.
However in Iran, perhaps surprisingly, support for the US-led forces remaining jumped from 36% to 74% in response to an Iraqi request.
Opinion matters
Any such survey is a snapshot of opinion at one particular moment.
It is evident that the terror threat has shot up
Bob Macdonald, London, UK
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With headlines on all sides about Iraq "drifting towards civil war", will people simply be confirmed in their opinions? Or will the drama of what is happening encourage them to think again?
Public opinion today matters like never before.
In part, this is because domestic politicians in many countries have drafted in the pollsters, analysts and methods of the commercial world to better understand the political market-place.
Washington's efforts to spread democracy around the world - especially to the Middle East - represents America's most ambitious foreign policy initiative since the bid to contain Soviet Russia at the outset of the Cold War.
In many ways, it is more ambitious, and it depends in large part on shaping attitudes.
Unfinished business
Given these results - especially those from Middle East, where three of America's major regional allies, Saudi Arabia, Egypt and Turkey, were included in the survey - there is still a great deal of work to do.
US diplomats are well aware of the problems. The way things in Iraq have turned out has inevitably complicated Washington's task.
Critics say that the US represents itself as the country of democracy, freedom and individual opportunity but, instead they argue, its standing has been tarnished in many peoples minds by Abu Ghraib and Guantanamo.
This points to an interesting problem: we are dealing here with perceptions, and perceptions are often complicated, even contradictory, and difficult to reduce to a simple answer.
There is no doubt, for example, that the Iraq war has shifted attitudes in the Middle East against Washington, even among its traditional friends.
Equally, the US way of life remains a pole of attraction for many ordinary people, and it's not just a question of jeans and Hollywood.
Consider one intriguing set of answers in this poll - those of ordinary Iranians on the question of US troop withdrawal from Iraq.
If requested by the Iraqi government, some 74% of Iranians say the US-led troops should stay, a level of support only rivalled by that in Australia, one of America's staunchest allies.
High stakes
So what does this mean? Well, for one thing, many Iranians may see the Shia element of the Iraqi government as being friendly towards them.
They may also fear instability on their borders. But equally we know from other opinion polls that the attitude of many ordinary Iranians - especially the young - to the US is remarkably positive.
Opinion polls appear to simplify, but in fact they provide yet another insight on an ever-more complex world. Thus measuring opinion is of vital importance to policy-makers and analysts.
In some ways, it is all not so new.
At the height of the Cold War, Nato used to conduct regular detailed surveys of opinion within its member countries to try to spot any shifts in public attitudes towards the alliance, defence spending and so on.
Today, the stakes are just as high. A whole new discipline has been created, that of "public diplomacy".
And it is a field where the traditional diplomat often sits side-by-side with the opinion pollster and the expert on social attitudes.
Sixty percent of respondents in an international survey conducted for the BBC World Service felt that the likelihood of terrorist attacks around the world has been increased by the war in Iraq.

The international polling firm ''GlobeScan'' conducted the survey, which polled 41,856 residents of 35 countries between October 2005 and February 2006. Participants were asked, "Has the war in Iraq increased, decreased or had no effect on the likelihood of terrorist attacks around the world?"

Fifteen percent felt that the likelihood or terrorism had decreased; 12 percent felt there had been no effect; and 13 percent did not answer.

Out of the 35 countries polled, only Mexico and Nigeria thought the invasion lessened the likelihood of terrorist attacks. By contrast, 85 percent of Chinese respondents said they felt the invasion increased the likelihood of terrorist attacks.

Other questions asked in the poll found that 45 percent of respondents felt removing Saddam Hussein from power was a mistake, compared to 36 percent who felt the removal was the right decision. The poll also found that results were split on whether the foreign troops should remain in Iraq until the country is stable: 35 percent said they believed the troops should stay, 32 percent felt the troops should pull out within a few months, and 13 percent thought that a pull-out should occur within a few months unless the government of Iraq requested them to stay.

"It's official. Citizens worldwide think Western leaders have made a fundamental mistake in their war on terror by invading Iraq," Doug Miller, president of ''GlobeScan'', said. "Short of the Iraqi government asking them to stay longer, people think the troops should leave," he said.

In the United States, the ''GlobeScan'' poll found that 55 percent thought chances of terror attacks were increased. In an unrelated poll conducted in the U.S. by ''CBS News'', only 36 percent of U.S. respondents thought "the war is going well," and that 30 percent felt "Bush was doing a good job of handling the conflict." This U.S. poll also found that only 18 percent held a favorable view of Vice-President Dick Cheney.

In a televised interview with Elizabeth Vargas of ABC's ''World News Tonight'' which aired last Tuesday, President Bush said, "If I worried about polls, I wouldn't be doing my job," on the topic of his low U.S. approval ratings. "I think the American people — I know the American people want somebody to stand on principle, make decisions and stand by them and lead this world toward a more peaceful tomorrow, and I strongly believe we're doing that," he said.  

"I've got ample political capital and I'm using it to spread freedom and to protect the American people, plus we've got a strong agenda to keep this economy growing." President Bush also said that Iraqis must choose between "chaos or unity."