The poll on Thursday by the independent Palestinian Centre for Policy and Survey Research showed Hamas was likely to take three of the four biggest districts in Gaza, including one where Palestinian President Mahmud Abbas’ dominant Fatah movement had been expected to triumph.
The election is seen as a test of strength between Hamas and Abbas.
Voter turnout topped 80% for the ballot in which candidates vied for 118 seats in the 10 municipal councils.
The pro-Hamas party list said initial results tallied by its own observers indicated that the group had won seven of the 10 municipalities.
A Hamas spokesman, Sami Abu Zuhri, praised the high turnout.
But Fatah sources disputed the exit poll predictions and said they thought they had won most of the races.
Hamas made a strong showing in municipal elections in the West Bank last month and the group may do even better in Gaza, where 1.4 million Palestinians live in often dire poverty.
Political analysts say that by taking part in the municipal elections, Hamas is also demonstrating its political sway – and claim to a share of power – before Israel’s planned withdrawal of settlements from Gaza.
The Palestinian electoral commission expects results to be announced for the Gaza municipalities on Friday.