The office of Hamas leader Ismail Haniya 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."
Haniya's deputy Saleh al-Arouri led a delegation to Cairo last week. 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.
It was hoped that reconciliation could alleviate humanitarian suffering in Gaza, home to some two million people.
The United Nations has signaled its support for a fresh reconciliation push.
Hamas won 2006 parliamentary elections but Palestinian President Mahmoud Abbas' Fatah and much of the international community refused to accept the result, leading to increased strife.