He said other conditions included the release of Hamas prisoners from Egyptian jails and a commitment that the US and other powers would recognise the outcome of elections if Hamas was to win.
"This has no place in an inter-Palestinian deal," Abed Rabbo said.
Hamas has not disclosed its position on unity talks and whether it will accept an Egyptian-mediated proposal, already endorsed by Fatah.
Fawzi Barhoum, a spokesman for Hamas, said the movement's response "will be taken within a framework aimed at guaranteeing the success of the Egyptian efforts".
The group, which has ruled Gaza since it seized control and pushed out Fatah over two years ago, had earlier criticised the deal for making "no reference to the struggle [with Israel] and the aggression against our people".
A Hamas delegation had been due to travel to Cairo on Sunday to give its response to an Egyptian-mediated unity proposal.
But sources told Al Jazeera that the visit had been delayed as Omar Suleiman, Egypt's intelligence chief who has been behind the unity talks, was away.
In his press conference on Saturday, Abed Rabbo insisted that Mahmoud Abbas, the Palestinian president, would call for elections, regardless of the Hamas position.
Asked by Al Jazeera how this could be done without a commitment from Hamas, he responded: "We will find a way. We want Arab and international monitors on every ballot box in the West bank and Gaza."
The Palestinian Basic Law mandates that a new general election be called at least three months before the end of the sitting parliament's mandate, a deadline which falls on October 25.
Abbas's four-year term expired in January, but his Fatah party cited provisions in the constitution that require presidential and parliamentary elections to be held together to justify his remaining in office.