Government spokesman Ghazi Hamad said the talks in Gaza which started late on Saturday on a document that would seal an understanding between the Palestinian factions would continue on Sunday, adding that the atmosphere was good.
Abbas's spokesman, Nabil Abu Rudeina, refused to tell journalists whether any agreement had been reached, saying: "The important thing is to reach an accord on the main questions that will get us out of this crisis."
He said it was necessary to reply to the demands of Western powers which have suspended direct aid to the Palestinian Authority after Hamas was elected to government.
Earlier, Rudeina said Hamas had agreed that resistance fighters should unilaterally stop firing rockets at Israel from the Gaza Strip.
But Sami Abu Zuhri, the Hamas spokesman, said: "This statement is inaccurate. The military wing has not given a commitment in this regard. The problem is with the occupation, not the Palestinian people."
Israeli air strikes have killed 15 civilians in Gaza in recent attacks aimed at resistance factions involved in firing homemade rockets into Israel.