"The Arab initiative is continuing, and as I said, there is some hope and we should cling to it and invest it," Moussa said before heading home to Egypt.
On Friday, he had chosen to delay his departure from Lebanon in order to continue talks.
Distrust between the anti-Syrian ruling coalition and Hezbollah-led opposition is growing after a 15-month political crisis and three months with no president.
Al Jazeera on Saturday quoted Sheikh Naim Qassem, the deputy secretary-general of Hezbollah, as saying that the government was ignoring constitutional norms and pushing the country towards collapse and corruption.
He accused the governing majority of incapacitating the Arab initiative and of seeking to implement a pro-American political project.
Moussa had undertaken three days of talks with political leaders, but was unable to break the deadlock and said the "sharpness of the tension" had to be fixed.
Politicians have agreed on a compromise candidate, General Michel Suleiman, the army chief.
Moussa said his selection was valid. However, the parliament must amend the constitution to allow a sitting military chief to be elected.
Moussa, on his second visit to the Lebanese capital this year, hosted the talks with Saad al-Hariri, the majority leader; Michel Aoun, the Christian opposition leader; and Amin Gemayel, a former president who is aligned with the anti-Syrian majority bloc.
The discussion focused on ways of implementing a three-point Arab League plan calling for the election of Suleiman as president, the formation of a national unity government and the adoption of a new election law.
The plan was unanimously adopted by Arab foreign ministers in Cairo, Egypt, last month.
Moussa said the two sides still supported Suleiman and showed "a common desire" to reach a solution to the presidential crisis, but he refused to say what issues were holding up an agreement.
An official close to Berri's entourage said he was trying to convince his camp to agree on a formula in which the ruling coalition, the Hezbollah-led opposition and the new president would each have 10 ministers in a new government.
The majority and the opposition had previously rejected this scenario with each insisting on having more leverage.