The Palestinian political factions Hamas, Islamic Jihad and the Popular Front for the Liberation of Palestine (PFLP) are at the Doha summit.
The meeting aims to establish an immediate ceasefire in Gaza and a proposed reconstruction fund for the territory.
By Friday morning 1,133 Palestinians had been killed since Israel launched its offensive on December 27.
Hashem Ahelbarra, Al Jazeera's correspondent in Doha, said the delegates in Qatar recognise the legitimacy of the Gazan factions, whereas Egypt, Saudi Arabia and Western nations have sidelined them from a ceasefire talks.
"You have two camps: The so-called moderate Arab countries, Saudi Arabia, Egypt, Jordan, some Gulf monarchies like the UAE, and those who are trying to say that we totally disagree with the US attempt to implement a new Middle East."
Ahelbarra said the former is uncomfortable with Hamas's ties with Iran and suspects that the Iranian leadership is using some Arab countries to further its influence in the region.
He said that the latter group believes it has the duty to convey the anti-war feeling of the Arab street and wants to condemn Israel's actions.
Talks are continuing in Cairo over an Egypt-sponsored truce, with Amos Gilad, the Israeli chief negotiator, reportedly telling Egyptian officials that Israel wants an open-ended ceasefire.
Israel demands that rocket fire from Gaza ceases and an international force preventing weapons from being smuggled into Gaza is established for any deal to be signed.
Livni, due to arrive in Washington DC on Friday, will meet Condoleezza Rice, the outgoing US secretary of state, to discuss a potential US role in stopping weapons smuggling.
- International force to stop weapons smuggling into Gaza
- Immediate halt to offensive
- Full withdrawal of Israeli troops from Gaza
- Re-open all crossing points into Gaza
- Lift Gazan economic siege
Hamas delegates have also been in Cairo, the Egyptian capital, reportedly offering a year-long, renewable ceasefire.
However, this offer is also subject to conditions: an immediate halt to Israel's offensive, a full withdrawal of Israeli troops from Gaza, the re-opening of all crossing points into Gaza, and a lifting of the economic siege.
Al Jazeera's Jacky Rowland, on the Gaza-Israeli border, said: "There is certainly momentum for a ceasefire.
"[But] as we get closer to an agreement, both sides are focusing on those little details that could make or break an agreement."