The Fund signalled faster engagement with both countries as support across the Middle East and North Africa widens.
Troops moved in after an overnight standoff at a depot, accompanied by protests and an unconfirmed report.
Lebanese leaders want peacekeepers to stay on as a third party between Lebanese and Israeli forces.
The decision removes the Iranian bank's authorisation to operate in the Lebanese market.
The first releases followed the ruling, among them a detainee widely known by the nickname "Doctor Food".
Sheikh Mohammed bin Abdulrahman Al Thani met Aoun, Berri and Salam during a visit to Beirut.
QatarEnergy and TotalEnergies will jointly develop the plant, with Qatar financing and operating it.
Governor Karim Souaid said talks are moving at a good pace and a breakthrough could come by year end.
Damascus says the man, known as the "Butcher of Baniyas", is in its custody and that the operation was coordinated.
The shelling hit two southern towns as tension along the Blue Line continued to build.
The US secretary of state intervened after a truckload of explosives was intercepted near Beirut.
Jean-Pierre Lacroix closed a three-day visit weeks before UNIFIL operations are due to end.
Israeli Defence Minister Israel Katz threatened to seize more territory in the south.
Residents and contractors are holding off on rebuilding while the threat of renewed fighting persists.
The two men were working in olive groves in the southern village when the munition detonated.
