However, 70% of Palestinians interviewed said they believed such attacks were sometimes justifiable.
The Global Opinion Trends survey , by the US-based Pew Research Centre, polled 45,000 people in 47 countries.
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It also found widespread optimism in poor countries that the next generation will enjoy better lives.
And it suggested that people viewed the US as the most friendly country in the world and the most feared.
In Lebanon, Bangladesh, Jordan, Pakistan and Indonesia, the proportion of Muslims who support suicide bombing has declined by half or more since 2002.
But in areas of conflict, the results are different – 70% of Palestinians said that suicide bombings against civilians were sometimes justifiable.
There is also declining support among Muslims for Osama Bin Laden. In Jordan, just 20% express a lot or some confidence in Bin Laden, down from 56% four years ago.
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However, the survey found broad concern among Muslims that tensions between Sunni and Shia are not limited to Iraq and represent a growing problem for the Muslim world.
The survey also suggests that as countries and families grow richer, optimism increases, as well as support for ruling governments.
In Latin America, the poll results indicate that despite the electoral success of a new generation of left-wing leaders, the majority of respondents believe that people are better off living in a market economy.