"We believe a positive spirit is prevailing, after earlier delays that we were concerned about, but I am confident that progress can be made in the coming days," Williams said in statements released by his office in Beirut.
Lebanese Prime Minister-designate Saad Hariri led his March 14 slate to a narrow victory over the March 8 opposition in June parliamentary elections, pledging to form a unity government quickly.
Ministerial disputes and political defections, however, derailed his efforts, forcing him to resign briefly following a decision to move ahead with a Cabinet without opposition consent.
Political dialogue has brought encouraging developments as Aoun expressed his support for "the open dialogue" from leading lawmakers.
2014: The Year in Music [PHOTOS]