Late on Tuesday, they also voted to change the electoral system, Aljazeera reported.
Two-thirds of the 132 members of parliament (MPs) voted in favour of a constituency-based voting system, while a third backed proportional representation, ahead of a full Palestinian Legislative Council debate on the issue on Wednesday.
Qadura Faris, a Fatah leader and a member of the Palestinian Legislative Council, told Aljazeera: "If the president has no remarks about the law, it may be effective starting from Wednesday.
"The president has a different point of view over the methodology of the elections.
"If he (Palestinian President Mahmud Abbas) insists on his opinion, the Legislative Council may have a third review over the law. If he does not, the council may sign and approve the law on Wednesday immediately after the second review," he added.
The Palestinian Central Elections Committee (CEC) had been hoping to see the law amended by 17 April.
The go-ahead for the crucial 17 July vote comes amid fears by some MPs that elections could be delayed.
Earlier, some officials had voiced their reservations about elections being delayed.
Both Abbas and the Hamas movement strongly protested against any vote delay.
But Fatah MPs said parliament could not change the election date.
"Only Palestinian Authority President Mahmud Abbas can change the date of the vote," MP Dalal Salama said.
"Most Fatah deputies are in favour of holding the elections on the planned date, 17 July, so for that to happen, the electoral law must be adopted as quickly as possible," Fatah deputy Ahmad al-Dik said.
Fatah holds 62 seats in the 83-seat parliament.