Carriers said they were assessing the situation on Sunday morning with several airlines including Qantas, Jetstar and Virgin resuming flights, which were disrupted after the volcano sent a grey-black plume of ash and steam at least 1,500 meters into the sky.
Flights affected also included those operated by KLM and AirAsia.
Routes to Bali from several cities in Australia, the Netherlands and Malaysia were canceled and re-routed on Saturday night and early Sunday morning as a result of the eruption.
Jetstar said its pilots had determined the improved conditions in Bali to be safe for flying.
"Most scheduled flights to and from Bali today will operate," Jetstar said in a release on its website.
Jetstar added a warning to passengers that because both the volcano and the ash cloud movement were highly unpredictable, flights could be subject to change at short notice for safety.
The latest eruption produced a bigger ash cloud than the initial eruption on Tuesday, Indonesia's Disaster Mitigation Agency said.
It has called for calm among the local community, from which around 25,000 people have been evacuated from the slopes of Agung to hundreds of refuge shelters.
After Tuesday's eruption, Singapore had updated its travel advisory for the island, warning that ash clouds could "severely disrupt air travel".
Bali, famous for its surf, beaches and temples, is located on the Pacific ring of fire, a seismically active belt where a large number of earthquakes and volcanic eruptions occur.
It attracted nearly 5 million visitors last year, and Bali's Denpasar International Airport hosts a large number of air traffic.
Tourism, a cornerstone of Bali's economy, is Indonesia's fourth-biggest earner of foreign currency after natural resources such as coal and palm oil.
Agung, the highest point on the island, towers over eastern Bali at a height of just over 3,000 metres. When it last erupted in 1963 it killed more than 1,000 people and razed several villages.
Indonesia has nearly 130 volcanoes, more than any other country. Many of them show high levels of activity but it can be months before an eruption.