Hamas leaders in Gaza, who have the most to lose from the unity deal, had objected to relinquishing power to Abbas. The group has employed tens of thousands of people in official posts in the territory who now face integration into larger Palestinian bodies that might be headed by Abbas loyalists.
While the deal might still face opposition from the Hamas rank-and-file, Rishq suggested that the movement's leaders were now on board.
Abbas and Mashaal met later Wednesday in Cairo to discuss the next steps in the deal, including formation of an interim government to be made up of politically independent technocrats. Such a composition is meant to lower the profile of Hamas, which the West shuns as a terrorist organization.
A Hamas-run TV station in Gaza quoted Mashaal as saying that the meeting was positive and that he and Abbas were moving in the right direction for the good of the Palestinians.
Abbas enjoys the support of the United States and European countries, but it remains unclear how much he would lose if reconciliation with Hamas moved forward.
Israel and the international community have said they will not deal with Hamas unless it renounces violence and recognizes Israel.
By forming an alliance with Hamas, Abbas risks losing hundreds of millions of dollars in international aid, though Palestinian officials hope that signals of moderation from Hamas will make the new government acceptable to the West.