The call for elections was made in a joint statement at the end of two days of closed-door talks attended by representatives of 13 leading political parties.
The factions called on the electoral commission to prepare for presidential and legislative elections to be held by the end of next year at the latest.
They asked Palestinian president Mahmud Abbas to set a date for the polls after consulting with all sides.
The Egyptian-sponsored agreement is aimed at ending the 10-year rift between them, and calls on Hamas to cede power in the Gaza Strip to Fatah by December 1.
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The statement said the reconciliation deal between the Islamist movement Hamas and Abbas's Fatah party was a "realistic start to end divisions".
It underscored the "importance of removing all obstacles in the path of the government's efforts to immediately assume its responsibilities towards our people".
There have been no Palestinian parliamentary elections since Hamas seized control of Gaza in 2007 from Fatah, which dominates the Palestinian Authority government in the Israeli-occupied West Bank.
The agreement faces significant stumbling blocks, in particular the future of Hamas's vast armed wing, which has fought three wars with Israel since 2008.
Abbas has repeatedly said he would only accept one military authority in the Palestinian territories, but Hamas officials have refused to disarm.
Israel -- which has maintained a crippling decade-long blockade of Gaza -- has also said it would not accept any Palestinian government that includes Hamas unless the Islamist group puts down its weapons.