The poll indicates Fatah won more than 42 percent of the vote and Hamas at least 34 percent. It was based on a survey of 6,500 voters with a margin of error of five percentage points.
Official results are not expected for several hours.
Palestinian leader Mahmud Abbas, who heads Fatah, said he is ready to resume peace talks with Israel, even if Hamas joins the government.
In the past, Hamas has claimed responsibility for several suicide bombings against Israel. It has refused to accept the existence of the Jewish state.
(compiled from agency reports)