In private talks, officials cautioned against high expectations from the outcome of the talks as the two factions remain divided over key points in the Yemeni initiative.
Yemen's new plan
Hamas and Fatah had initially accepted the plan as a blueprint for peace, but showed concern over the logistics of how the Palestinian Authority (PA) would restore control over Gaza.
Saleh's revised plan stated that a solution should be wide-ranging, similar to what the factions had reached in Cairo in 2005, as well as the Saudi-sponsored Mecca accord that led to the formation of a short-lived Palestinian unity government earlier last year.
The plan aims to promote "the unity of the West Bank and Gaza," currently split between the two factions, and the unity of the PA through a single government in both Palestinian territories.
The revised plan also calls for the restructuring of Palestinian security, with forces intended to come under government and PA control rather than Palestinian factions.
A committee comprising of several of Arab countries would then follow up the implementation of the Cairo and Mecca deals.
Yemen and other Arab states supporting an inter-Palestinian dialogue would "put pressure" on Fatah and Hamas to resume talks on the basis of the Yemeni blueprint, a source told Al Jazeera.
While the two delegations accepted the initiative as a blueprint for peace, they disagreed on practicalities that would restore control of the Palestinian Authority over the Gaza Strip.
An unexpected upheaval, unrelated to the initiative itself, came when Abbas sent a delegation of the Palestine Liberation Organization (PLO) to the talks in Sanaa, which had prompted Hamas to initially refuse any negotiations.
The PLO, which was established in 1964, is internationally recognised as the sole representative of the Palestinian people.
Hamas, which emerged from Gaza in 1987, existed outside of PLO's framework, making them a force difficult to reconcile with.
But Hamas and the other Palestinian factions reached an agreement in 2005 Cairo talks which achieved their representation within the PLO.
Meanwhile, Hamas insists that Yemeni negotiations stay between Fatah and Hamas in order for their differences to be resolved.