In a speech to the UN General Assembly, President Michel Aoun asked that Lebanon be designated as a global centre for dialogue.
The country's top court convicted a 'terror cell' of links to Iran and Lebanese militia Hizbullah, and of plotting terror attacks in Kuwait.
The UAE is calling for a 'change of behaviour' but not 'regime change' in Qatar, minister for foreign affairs said.
New terror blacklist accuses Qatar of supporting 59 people and entities linked to 'terrorism', a charge which Qatar rejects.
A senior UAE official said the measures taken against Qatar this week were not aimed at seeking new leadership in Doha.
Jordan is hosting the Arab League summit, where discussions are expected to focus on Middle East peace and regional challenges such as terrorism and the refugee crisis.
Two days of indirect talks in Kazakhstan have yielded a ceasefire mechanism, but a lasting political solution to the Syrian conflict is still elusive.
Civil society leaders hope the UN accepts an initiative to name Lebanon an international centre for dialogue and conflict resolution.
The two states set up a co-ordination council to enhance collaboration on key regional challenges, including the threat posed by extremist groups.