But prominent Islamic group Hamas stayed away from Tuesday's meeting.
"Definitely, there is a possibility that we can reach an agreement on basic political common denominators," Abbas said after a meeting of his PLO Executive Committee attended by Islamic Jihad leader Muhammad al-Hindi.
Abbas' efforts appeared to represent an attempt to bring Hamas and Islamic Jihad - groups behind dozens of anti-Israel attacks during a four and a half year uprising - into the political mainstream to help his peace efforts with Israel.
However, Israel has called on Abbas to dismantle resistance groups rather than embrace them.
Hamas and Islamic Jihad, opposed to Israeli-Palestinian negotiations, hold to a vision of an Islamic state incorporating what is now Israel.
Talks on whether the two factions would join the PLO kicked off last month in Cairo, where resistance groups agreed to extend a ceasefire with Israel until the end of the year.
But after the Gaza meeting, al-Hindi said "a long time and much effort" is needed before Islamic factions can agree to membership of the PLO.
Abbas's organisation, an umbrella group of secular factions, is the Palestinians' main policy-making body.
Hamas, the most powerful resistance faction, said it had not sent a representative to the meeting due to "technical reasons".
Mahmud Abbas wants resistance
groups to join the mainstream
However, Abbas said Hamas is expected to attend a meeting next month that will include committee members and Islamic Jihad.
He gave no time-frame on how long the membership process might take.
Both Islamic groups have long boycotted the PLO, citing its peace moves with Israel. But they have recently declared a readiness in principle to join if a series of conditions are met.
Al-Hindi said membership talks should focus first on "reforming" the PLO.
The charter of the PLO, founded by Arafat in the 1960's, calls for creation of a Palestinian state only in territories captured by Israel in the 1967 Middle East war.