A poll by the West Bank's Bir Zeit university forecast that Fatah had won 63 seats in the 132-seat parliament against 58 for Hamas.
Fatah won 31 of its seats from voting on national lists while the other 32 were elected in constituencies, the poll said. Hamas won 26 seats in the national lists and another 32 in constituencies.
The small leftist Popular Front for the Liberation of Palestine would win three seats while three other minor parties should win two seats each, the Bir Zeit pollsters said.
Another forecast by the Ramallah-based Palestinian Centre for Policy and Survey Research said Fatah won 42 percent of votes against 35 percent for Hamas, but failed to give a breakdown of seats.
It also forecast that the PFLP had come third with five percent of votes.
The exit polls were released around an hour after all polling stations in the Gaza Strip, West Bank and annexed east Jerusalem were closed.
More than three-quarters of the registered voters cast their ballots, the organisers said after all polling stations were closed.
Ahmed al-Dweik, director general of the central elections commission, told a press conference in Ramallah that around 1,035,000 people had voted in the second ever general election, representing 77.6 percent of the 1.35 million-strong electorate.
The turnout in the Gaza Strip reached 81.65 percent while the figure for the West Bank, which includes annexed east Jerusalem, was 77.3 percent.
Voting had been extended for two hours in east Jerusalem after the doors were closed on polling booths in the West Bank and Gaza at 1700 GMT.
Voting was continuing for a further two hours in annexed east Jerusalem after election organisers said that the Israeli authorities had prevented some voters from casting their ballot on time.
Palestinian leader Mahmud Abbas called the poll a decisive step on the road to independence, a view echoed by Israel's acting leader Ehud Olmert, who urged voters to shun "extremism", a reference to Hamas which is contesting a parliamentary election for the first time.
The possibility of a Hamas win, or a strong enough showing to secure a seat in cabinet, has prompted Israel to warn it will not deal with a government that includes a "terrorist organisation".
After casting his ballot, Abbas said the exercise in democracy should strengthen the prospects of peace and pledged his readiness to resume negotiations with Israel.
"The Israelis should have no reason to be fearful but rather pleased as we are building a democracy which can serve as a base for peace between us.
"After the elections I will form a new government and I am always ready for negotiations with the Israelis although they must want them on their side."
Hamas's top candidate Ismail Haniya vowed that the militant movement would not disarm after entering parliament.
"The Americans and the Europeans say to Hamas: either you have weapons or you enter the legislative council. We say (we will have) weapons and the legislative council. There is no contradiction between the two."
Hamas, campaigning on a Change and Reform banner, has sought to cash in on disillusionment with Fatah over the stalled peace process, corruption and by claiming its fighters forced Israel to pull out of the Gaza Strip last summer.