A win by Hamas will pose a great problem for international efforts to restart peace talks with Israel, analysts say.
American President George W Bush said the US would not deal with Hamas unless it renounced its call to destroy Israel and European leaders echoed the call for Hamas to renounce violence.
"I've made it very clear that the US does not support political parties that want to destroy our ally Israel," President Bush said.
Mr Bush added that the poll was a "wake-up call" for the Palestian leadership, but he hoped Palestinian leader Mahmoud Abbas would stay in power.
Israel has stated it will not deal with a Palestinian Authority, which includes Hamas.