At the end of Wednesday's talks, Hamas agreed to set up talks with President Mahmoud Abbas's Fatah on Thursday.
Hamas made a strong showing in recent municipal elections only to see victories in three Gaza Strip towns quashed by a court after Fatah allegations of fraud.
Palestinian judges ordered a rerun of the vote in some districts that is set for 1 June. But some ordinary Palestinians fear the dispute could escalate into violence.
Senior Hamas leader Mahmoud al-Zahar had initially described the crisis with Fatah as "difficult", but Hamas's tone softened after a second round of talks on Wednesday. Direct talks with Fatah could reduce the threat of factional conflict.
End to crisis
"We are intent on ending this crisis," said Hamas political leader Saeed Seyam after the second round of talks, which Zahar did not attend.
"It is a positive step that there will be a meeting between the two parties under the auspices of the (Egyptian) brothers. We hope it will result in positive steps toward preserving the unity of our people."
Tens of thousands of Hamas supporters rallied in Gaza on Monday against the court rulings. Hamas has accused Fatah of pressuring judges to overturn results not to its liking.
Fatah officials, after meeting the Egyptians on Monday, urged Hamas to stop holding protests and engage in dialogue but said the court election rulings were not up for discussion.
International monitors said on election day that they uncovered no serious irregularities.
Egypt has been a key intermediary in the Israeli-Palestinian conflict and in Palestinian factional disputes.
Cairo helped nudge fighter groups into a ceasefire with Israel this year and has offered to secure the Gaza Strip's southern border after a planned pullout of Israeli settlers from the area this August.