Israel's refusal to allow East Jerusalem's Palestinians to vote on 25 January had drawn calls from some officials for a postponement - which could suit Abbas's divided Fatah movement very well, but not Hamas as it rides a surge of popularity.
Israel opposes participation by Hamas, an Islamic group sworn to its destruction. Abbas still says he wants the vote to take place on time.
Donors have been pushing for the long-delayed parliamentary
ballot to strengthen democracy - the last was held in 1996 - but they are also wary of Hamas doing very well.
Hamas and the other factions, not including Fatah, said in a statement on Thursday that Abbas should first bring international pressure on Israel to ensure that East Jerusalem residents are allowed to take part. If that fails, he should find another solution.
Mushir al-Masri, a Hamas spokesman in the Gaza Strip, said: "We have to find a way, a mechanism, to press ahead with the election despite the Israeli decision.
"Delaying the parliamentary election will create internal disruption and will spell the end of any Palestinian dialogue."
Hamas did not say how it thought the East Jerusalem problem could be solved if Israel stuck to its line.
Hamas members are expected to
do well in the parliamentary vote
One suggestion is that deputies could be appointed for the six seats representing Jerusalem districts in the 132-member parliament, political analysts said.
Nabil Shaath, the senior Palestinian official, said on Wednesday: "We cannot hold elections anywhere if the Palestinians in Jerusalem are not allowed to vote."
In the southern Gaza Strip, armed men from al-Aqsa Martyrs Brigades - part of Fatah - held a news conference urging factions to rally behind the idea that the election must be delayed if there was no participation in Jerusalem.
Hamas has been boosted ahead of the election by division in Fatah between veteran leaders and younger members, as well as by a popular feeling that the Islamic group, which is behind a resistance bombing campaign, is less tainted by corruption.
Israel says all Palestinian political activity in East Jerusalem was banned under the accords. Palestinians dispute this position.
Israel captured East Jerusalem in the 1967 Middle East war and annexed it in a move not recognised internationally. It sees it as part of its capital. Palestinians want it as the capital of an eventual state.