West Bank-based Palestinian prime minister Rami Hamdallah is to make his first visit to Gaza since 2015 on Monday, aiming to crown a rapprochement between the rivals after a decade of animosity and outbreaks of violence.
Official Palestinian news agency WAFA said Hamas head Ismail Haniya called Abbas on Sunday evening to discuss preparations for Monday's visit, but it did not give any details.
The initiative is backed by Egypt which will be closely following the talks, intended to prepare for a transfer of power in the Gaza Strip from Hamas to Abbas's Palestinian Authority (PA).
"An Egyptian delegation, including Egypt's ambassador to Israel Hazem Khairat, and two other high ranking Egyptian intelligence officers, arrived in Gaza" from Israel, Mohammed al-Maqdama from the PA office that coordinates with the Israeli authorities told AFP.
Hamas said in a statement that Haniya and Hamas Gaza chief Yahya Sinwar met the Egyptians on their arrival.
Palestinian media reports said that PA culture minister Ehab Bessaiso also arrived, taking charge of his ministry's Gaza offices and meeting staff.
Hamas and Fatah, which dominates the PA, have both expressed confidence that the latest unity initiative will fare better than the failures of the past.
Hamas, blacklisted as a "terrorist" group by the European Union and the United States, won a landslide victory in 2006 Palestinian parliamentary elections.
It ousted Fatah from Gaza the following year after wrangling over the formation of a new government degenerated into bloody clashes.
Since then, Abbas's limited power has been confined to the West Bank which is under Israeli military occupation and is located, at its nearest point, 40 kilometres (25 miles) from the Israel-Gaza border.
The Palestinian schism is seen as a major obstacle to a peace agreement between Israel and a future Palestinian state combining the West Bank and the Gaza Strip.