Hariri's office and Saudi-owned media said he flew to the UAE, a Saudi ally and fellow Gulf monarchy, on Tuesday.
Fly Baghdad, the first low cost airlines in Iraq, launched their first flights to Jordanian capital Amman on the second of this month.
Lebanon's fragile economy has one of the world's highest debt-to-GDP ratios and is underpinned by its banking system.
Lebanese Prime Minister Saad al-Hariri quit in a surprise broadcast from Saudi Arabia
Lebanon has been thrust to the centre of regional rivalry between Saudi Arabia and Iran
Comments came following the interception of a missile fired towards the Saudi capital Riyadh on Saturday.
Hariri meets Saudi king after announcing exit in Saudi Arabia
The state is able to finance itself, the FM said
Lebanese Finance Minister Ali Hassan Khalil said a fall in cash price of Lebanon's U.S. dollar-denominated bonds on Monday was no cause for concern.
Salameh told LBC there was no danger to the Lebanese pound, which is pegged to the U.S. dollar.