Fatah and Hamas have tried for months to agree on a national unity government, in hope of ending a boycott by the United States and the European Union and in order to present a united front towards Israel.
Washington and Brussels consider Hamas to be a terrorist group and suspended direct financial aid to the Palestinians because the movement refuses to renounce violence or recognise Israel.
Al-Rashq had earlier said in an interview with Al Jazeera that the two parties are ready to reach an agreement on the disputed issues.
"The meeting is an attempt to reach final solutions and agreements over a group of proposed cases, between the two sides, which are related to the formation of a national unity government, the ministries and the political programme," al-Rashq said.
"We can send an important and assuring message to the sons of our people that this meeting will help in reinforcing the national unity and avoiding any conflict between the two sides."
Tensions between the two factions, which had already claimed a number of lives, boiled over in the Gaza Strip in December, killing more than 30 people in that month alone.
However, violence has tapered off in the past couple of weeks.
Clashes in December began after Abbas called for early elections as a way of resolving the standoff with Hamas, which rejected the move.
Meeting with Syrian leader
Abbas's meeting with Bashar al-Assad, the Syrian president, reportedly ended amicably with the Syrian leader re-affirming his commitment to the Palestinian cause.
Briefing reporters in Damascus, Nabil Amir, Abbas's spokesman, said the two leaders had an "amicable and very frank" discussion that focused on "Palestinian issues in detail and the regional situation."
He reported that Assad had told Abbas that he was "attached to Palestinian national unity and ready to support anything that could help reinforce it, as well as efforts to find an adequate solution to the Palestinian problem."
Syria hosts the exiled leadership of a number of Palestinian groups and could exert considerable influence over Hamas. Meshaal moved to Syria from Jordan after an Israeli assassination attempt in 1997.