The first official poll gave Fatah more than 46%, compared to 39.5% for Islamic militant group Hamas.
The real results may not be announced for several more days.
The BBC's James Reynolds in Ramallah says whatever the final outcome it is clear Fatah is no longer the single dominant force in Palestinian politics.
That is because Hamas has now managed to convert its own long-standing popular support into a formal political voice, our correspondent says.
Both Fatah and Hamas have said they will consider a coalition if there is no clear winner.