The poll was conducted by prominent pollster Khalil Shikaki, and was said to have a 3 percent margin of error.
Hamas and Fatah have made several attempts at unification, which have broken down due to irreconcilable disagreements over which party should take power.
In an attempt to bring Hamas to heel in Gaza, Fatah cut salaries to Hamas-loyal government employees in the region by 30 percent, causing a financial crisis.
Hamas staged a bloody coup against Fatah, taking over Gaza in 2007, and attempted to assassinate PA Prime Minister Rami Hamdallah in Gaza in March.
