The USA Today/Pew Research Center poll taken Wednesday through Sunday found 54 per cent in favour of prosecuting Edward Snowden, the former contractor for the National Security Agency.
Some 38 per cent in the poll said Snowden should not be prosecuted.
The survey also found that a similar majority, 53 to 41 per cent, agreed with US government officials who said the programmes have helped prevent terrorist attacks.
But the poll respondents were divided on the question of whether they approve of the programmes, believed to include wide-ranging electronic surveillance of emails, other electronic messages and phone calls.
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"The more people learn about this, it could affect their final judgment on whether the government was right or wrong to do what it's been doing," said Michael Dimmock, director of the Pew Research Center for the People and the Press.
"What I think you're seeing in a lot of the surveys is that the public isn't particularly happy about this programme, particularly in the realm of civil liberties and privacy, but a lot of people are willing to give the government a certain amount of leeway in fighting against terrorism."
President Barack Obama defended secret US security programmes in an interview that aired yesterday, and rejected comparisons with former US president George W Bush.