This came in an opinion poll released by the Ram Allah-based Near East Consulting Institute on Monday.
The survey also found that 84% of those surveyed in the West Bank and Gaza Strip want a peace agreement with Israel while 86% want Mahmoud Abbas, the moderate Palestinian Authority president, to remain in his post.
The Islamist movement Hamas, which has been behind most attacks against Israel during a five-year uprising, has come under growing pressure to drop its charter's call for the destruction of Israel in the wake of its landslide victory last week over the secular Fatah party.
While Hamas's international reputation is based on its campaign of attacks against Israel, its popularity in the West Bank and Gaza stems in part from its providing a safety net for some of the poorest Palestinians.
Rather than indicate backing for Hamas's hard-line tactics, the survey found that 73% of respondents believed that Hamas should "change its position on the elimination of the state of Israel".
86% of Palestinians want Abbas
to remain in his post
Not only did an overall 84% support a peace agreement with Israel, but 77% of Hamas voters also wanted a settlement.
Israel has ruled out any prospect of negotiating with a Hamas government that refuses to accept its right to exist and continues to advocate violence, even though Hamas has not carried out any attacks for over a year.
A total of 1200 people were questioned in the survey which has a 3.5% margin of error.