Moussa was also to hold meetings on Friday with Nabih Berri, the Shia parliament speaker; Nasrallah Sfeir, the Maronite patriarch; and Fouad Siniora, the Lebanese prime minister.
The head of the 22-member Arab League, Moussa returned to Beirut on Thursday night after talks in Damascus with Bashar al-Assad, Syria's president.
Moussa said he was very satisfied with Syria's support for his efforts to mediate, but Beirut newspapers on Friday said Moussa's visit to Damascus had not led to any breakthrough.
"The same obstacles endure concerning the four objects of Arab mediation," the pro-government daily An-Nahar said, naming the international tribunal to try the suspected killers of Rafiq al-Hariri, a former Lebanese prime minister, the current government crisis, and presidential and legislative elections.
It also cited an international conference in Paris in January on aid to Lebanon after the 34-day war in July and August between Israel and Hezbollah, a Lebanese Shia political party and armed resistance movement
The opposition daily Al-Akhbar said the "chances of a rapid solution are dwindling because of the obstinacy of those in power".
Lebanon's political crisis erupted in mid-November with the resignation of six pro-Syrian cabinet ministers.
The ministers quit in protest at what they felt was the political marginalisation of Hezbollah and Amal, both Shia parties, and the Free Patriotic Movement, a Maronite Christian party.
Emile Lahoud, Lebanon's president, and Berri, both pro-Syrian figures, now consider the pro-Western government to be illegitimate.