The Palestinian militant group, Hamas, and 10 other factions have called on the Palestinian leader, Mahmoud Abbas, not to delay January's elections.
Hamas has not previously contested parliamentary elections
Palestinian officials have said they might cancel the poll in response to Israel's decision to bar Palestinians in East Jerusalem from voting.
Israel said it was concerned that Hamas might gain power.
In a statement, the groups urged Mr Abbas to find a way to ensure that people in East Jerusalem could vote.
They said Mr Abbas should try to win international support to put pressure on Israel, but if that failed he should try to find another solution.
"We have to find a way, a mechanism, to press ahead with the election despite the Israeli decision," Hamas spokesman Mushir al-Masri said.
"Delaying the parliamentary election will create internal disruption and will spell the end of any Palestinian dialogue," he added.
Scheduled for 25 January; originally set for July 2005
132 members elected to Palestinian Legislative Council (PLC)
Fatah and Hamas are main contenders
First time Hamas participates in parliamentary poll
Israel says Hamas cannot take part under a 1995 agreement
Last parliamentary elections held in 1996
Correspondents say Hamas wants the elections to go ahead as planned, to capitalise on its current surge in popularity.
They say a delay would suit Mr Abbas's divided Fatah movement - which did not join Thursday's call - as it would give extra time to try to heal internal rifts.
Chief Palestinian negotiator Saeb Erekat said the 25 January election would be sabotaged if Palestinians resident in East Jerusalem were prevented from voting.
Israeli officials have warned that the peace process will end if Hamas becomes the dominant Palestinian political party.
The election would be only the second since the Palestinian Authority was established in 1995.
Hamas' charter commits it to the destruction of Israel, and the group has been responsible for most of the suicide attacks inside Israel.