Israeli commentators were divided on whether Hamas's move represents a victory or a setback for the movement.
Is a Palestinian real reconciliation finally possible?
Hamas has sculpted itself as the only legitimate resistance to Israel's ongoing occupation.
"I won't accept the reproduction [in Gaza] of the Hezbollah experience in Lebanon", Abbas said, referring to the Lebanese armed group and political organisation that controls much of the country's south.
A Palestinian man surveys the scene of an Israeli airstrike at a Hamas outpost in the central Gaza Strip October 9, 2017.
The rocket was believed to have hit southern Israel on late Sunday but actually fell inside the airspace of the besieged Gaza Strip due to a suspected mechanical failure.
Leaders of both rival groups said in separate press statements that the first session of dialogue will be held at the Egyptian Security Intelligence Headquarters in Cairo on Tuesday, and that the sessions will be indoors and the press won't be able to attend or cover. Although the reconciliation was announced last week, there have been no good-will gestures so far.
Abbas wants his government to regain full control before reversing the measures, but Hamas wants them lifted immediately. The IDF later said they were false alarms. The remaining contentious issues will be discussed during a subsequent round of talks. Egypt has been pressuring Hamas and the Palestinian Authority to reach a rapprochement. While this provoked Hamas' condemnation, it did not affect reconciliation for now.
Fatah and Hamas, the two main Palestinian political parties, split violently in 2007.
This act of reconciliation appears to be more in progress than the effort in 2014, with the Gaza government being disbanded willingly by Hamas with the aim of putting it under the unity government, awaiting an election.
Other commentators said Hamas has fooled Fatah and Egypt.