Local election commission spokesman Firas Yaghi said counting had been completed in 21 of the 26 municipalities and localities where elections were held on Thursday.
"Fatah is in the lead, followed by Hamas, some independents and the Popular Front for the Liberation of Palestine (PFLP)," Yaghi said, adding: "Hamas are beating Fatah in some localities.".
Some 84% of a possible 140,000 eligible Palestinians had cast their votes, he said.
Vote-counting in Balaa township, in the east of Tulkarim, northern West Bank, showed that eight candidates with close ties to Hamas have emerged as winners, Aljazeera has learned.
In Kafr al-Labid, a bloc calling itself Martyr Yasir Arafat won all the seats.
Results of the first local council elections in 28 years - seen as a litmus test for next month's presidential ballot and of support for the Hamas resistance movement - are expected to be officially announced on Saturday.
The vote marks the first time Hamas has participated in the democratic process, turning the election into a test of its popularity beyond its power base in Gaza and in comparison to Fatah.
Mahmud Abbas is widely tipped
to win the presidential election
Hamas boycotted the first Palestinian general elections in 1996 and has also excluded itself from the 9 January election to find a successor to Arafat as Palestinian Authority (PA) president.
Hamas rejects the whole Palestinian autonomy process with Israel under which the PA was launched.
PLO chairman Mahmud Abbas is overwhelming favourite to win next month's ballot, having been nominated as Fatah's candidate.