Presidential candidate Michel Suleiman wins backing of majority bloc in parliament.
The first meeting on Thursday between Berri and al-Hariri ended without any statements.
After a second meeting, Kouchner said: “Work continues, the meetings continue and we’ll brief you when the job is done.”
The leaders also discussed laws for a 2009 parliamentary election.
Sources said Friday’s vote could be delayed amid demands by Michel Aoun, a Christian leader whose Free Patriotic Movement (FPM) is allied to Hezbollah, that a consensus prime minister also be agreed.
Aoun seeks guarantees that the size of his parliamentary bloc – the largest of any Christian faction – be recognised in the new cabinet.
Aoun’s FPM is currently not represented in the cabinet of Fuad Siniora, Lebanon’s prime minister.
Siniora’s cabinet is already under-strength after ministers from Hezbollah and other Shia parties pulled out last November in protest at not having enough representation to veto cabinet decisions.
An ongoing political crisis between the March 14 majority and March 8-led opposition has paralysed Lebanon for more than a year.
Lebanon’s president must be a Maronite Christian in line with Lebanon’s confessional power-sharing system.
Suleiman, 59, is favoured by the opposition.
He was appointed army chief in 1998 when Syrian troops and security forces had a presence in Lebanon.
The March 14 majority declared its support for Suleiman on Sunday, dropping its opposition to a constitutional amendment needed to allow a senior public servant to become president.