One of the biggest polling exercises ever conducted has uncovered an overwhelming belief that the Iraq war has increased rather than decreased the chances of terrorist attacks.

The survey of 41,856 people in 35 countries, commissioned by the BBC World Service and published today, found about 60% of those polled shared this view. Only 12% thought the war had reduced the chances of an attack, with 15% saying it had no effect either way. In Britain, 77% of those questioned thought the terrorist threat had risen since the 2003 invasion.

There was overall support in 20 countries for US-led forces to withdraw from Iraq in the next few months unless there was a specific request by the Iraqi government for them to stay.

The removal of Saddam Hussein was branded a mistake by a majority in 21 of the countries. On average, 45% of those questioned agreed that removing him was a mistake, with 36% supporting the action. In Britain, 40% of those polled said it was a mistake, while 49% backed it.

Steven Kull, director of the Programme on International Policy Attitudes at the University of Maryland, which helped conduct the survey between last October and January, said: "Though the Bush administration has framed the intervention in Iraq as a means of fighting terrorism, all around the world most people view it as having increased the likelihood of terrorist attacks."

The biggest pullout call came in Argentina, where 80% favoured this. Those most in favour of US-led forces staying until Iraq was stable were the US and Afghanistan 58%, Australia 57% and Britain 56%.

In Baghdad yesterday, three people were killed and 11 wounded when a motorcycle packed with explosives blew up outside a Sunni mosque. In a separate incident, the Iraqi Islamic party, the largest Sunni political group, said the body of one of its officials, Waad Jassim al-Ani, had been found with signs of torture after being detained by a security agency.