The office of Hamas leader Ismail Haniyeh said he had spoken with Egypt's intelligence head Abbas Kamel to inform him of his movement's backing for a fresh Egyptian-brokered push.
A statement from the movement said the two men discussed the "latest developments in the Palestinian issue and especially the reconciliation file and humanitarian projects for the people of the Gaza Strip."
The Egyptians presented the plan last week to a delegation to Cairo led by Haniyeh's deputy Saleh al-Arouri. Then, the Hamas leadership held a meeting in the Gaza Strip Wednesday to discuss the plan.
According to unofficial sources, the Egyptian road map for reconciliation consists of four stages, the implementation of which will be done over four months. According to the plan, the Palestinian Authority will remove all the sanctions it imposed on the Gaza Strip, and the judicial and land systems on both sides will meet for discussion.
So far secularists Fatah have not officially responded to this fresh push for reconciliation.
A previous Egyptian-brokered deal, signed by Hamas and Fatah in October 2017, collapsed on implementation.
In March, the prime minister of the Fatah-dominated West Bank government survived a roadside bomb hitting his convoy in a rare visit to Gaza, with his allies later accusing Hamas of planning the attack.
It was hoped that reconciliation could alleviate humanitarian suffering in Gaza, home to some two million people.
The United Nations has signalled its support for a fresh reconciliation push, but diplomats have little optimism.
Hamas won 2006 parliamentary elections but Palestinian president Mahmoud Abbas's Fatah and much of the international community refused to accept the result, leading to increased strife.
A year later, Hamas violently seized control of Gaza. Since then two separate Palestinian civil administrations emerged.
Elior Levy contributed to this story.