The disaster mitigation agency's command post in Bali said the number of evacuees has swelled to about 122,500.
The figure is more than double the estimated population within an immediate danger zone but people further away are leaving too.
Those who have fled are scattered in more than 500 locations across the island famed for its beaches, lush green interior and elegant Hindu culture, taking shelter in temporary camps, sports centres and other public buildings.
The exclusion zone around the mountain extends as far as 12 kilometre from the crater in places.
"I was very worried about the situation" said Nyoman Suarta, who was leaving a village a few kilometres outside the official no-go radius.
"So I decided to get out to save myself with my stuff and my pet," he said, carrying a cage housing a bird.
Agung, which dominates the landscape in the northeast of the island, last erupted in 1963, killing more than 1,100 people. It remained active for about a year.
"I would definitely be following the advice to stay outside the exclusion zone," said Heather Handley, an assistant Earth sciences professor at Sydney's Macquarie University.
The increase in tremors suggests an eruption is "imminent," she said.
Its eruptions in 1963 produced deadly clouds of searing hot ash, gases and rock fragments that travelled down its slopes at great speed.
Lava spread for several kilometres and people were also killed by lahars rivers of water and volcanic debris.
"If Mount Agung erupts, I'm in charge of pressing the alarm button," said Nyoman Kasna, a local official. "Sirens will sound and tell the community the mountain has erupted."
Agung, about 70 kilometres to the northeast of the tourist hotspot of Kuta, is among more than 120 active volcanoes in Indonesia.
Another volcano, Mount Sinabung on Sumatra, has been erupting sporadically since 2010, sometimes blasting volcanic ash several kilometres into the air and forcing more than 30,000 to evacuate their villages.
Indonesia, an archipelago of thousands of islands, is prone to seismic upheaval due to its location on the Pacific "Ring of Fire," an arc of volcanoes and fault lines encircling the Pacific Basin.
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