Abbas wished Rami Hamdallah, who has been prime minister of the Palestinian Authority since June, "success in carrying out this difficult task" during their meeting in Ramallah.
Hamdallah will have five weeks to name his new cabinet. Talks between Fatah and Hamas officials in the Gaza Strip since their reconciliation have already largely decided on the composition of the new government.
The two rival factions have been at odds since June 2007, when Hamas' militias overthrew Abbas' forces and took control of Gaza. At the time, Hamas leader Ismail Haniyeh was serving as prime minister of the Palestinian government following his movement's sweeping victory in 2006 legislative elections.
After the Gaza takeover, Hamas set itself up as the sole authority in the coastal strip, establishing fully staffed government ministries and security forces.
Several attempts at reconciliation failed until the two camps' surprise announcement April 23 that they had agreed to form a unity government headed by Abbas and composed of independent technocrats.
Abbas had been widely expected on Thursday to not only ask Hamdallah to form the transitional government but also to name and swear in its cabinet ministers. But Jamal Muheisen, a member of the Fatah Central Committee, said last-minute differences over filling some posts, including foreign minister, delayed the announcement.
Abbas reportedly wants to keep his incumbent foreign minister, Riyad Malki, while Hamas wants him replaced.
Muheisen said the transitional government will prepare for presidential and legislative elections, which according to the April agreement are to be held six month after its formation. More serious issues dividing the two parties will be resolved by the post-election government.
However, political commentator Hani Masri raised doubts about whether the elections will be held in six months and said the reconciliation talks "focused on procedural steps to end the division and ignored or postponed the more critical issues."
He was referring in part to the fate of Hamas' 40,000-strong public servants, including security forces. The overburdened and already heavily-staffed Palestinian Authority cannot afford to pay salaries of additional employees.
Speaking in Gaza, Hamas leader Haniyeh said Thursday that while he will give up his post as prime minister of the coastal strip when the unity one is formed, Hamas, nevertheless, will not be giving up its control over Gaza, which raised questions about the degree to which the divisions will end on the ground as well as on paper.