Sutopo Purwo Nugroho, the agency's spokesman, said evacuees are spread across more than 370 locations on the island, including temporary camps, sports centres, village halls and the houses of friends and relatives.
She said: "The tourists I have spoke to seem very anxious, I think this is due to having a better understanding and awareness about the dangers involved with an eruption".
Despite imminent danger, however, thousands of others were still refusing to leave for fear that their possessions, including cattle, would be stolen, officials said.
All outdoor activities, such as hiking and camping, have been suspended around the crater in East Bali and an exclusion zone has been set up 9-12 kilometres from the 3000-metre-high volcano, which last erupted in 1963. It may remain there and slowly cool to form an intrusion (most typical scenario) or could lead to an eruption an time.
"Instrumentally we have never recorded such high energy or seismicity from Mount Agung", Devy Kamil Syahbana, a seismologist from Indonesia's center for volcanology and geological hazard mitigation, told the Guardian. He said an eruption is a "definite possibility".
Authorities have urged people to stay out the danger zone, a designated 9km-12km radius of the volcano.
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The volcano is one of the most active in the region's Ring of Fire seismic zone and experts predict it will erupt in coming days, prompting the government to take precautions to prevent a repeat of its last eruption in 1963 which killed 1,600 people.
An increasing frequency of tremors from the volcano indicates magma is continuing to move towards the surface.
It is the highest point on the island, dominating the surrounding area and affecting local weather, particularly rain patterns.
"We have already sold our cattle, because we thought it was better than leaving them there for nothing", he said.
Bali's Ngurah Rai worldwide airport, which is about 76km from the volcano, remains open, with flights running as normal on Tuesday.
It is among more than 120 active volcanoes in Indonesia.
Virgin Australia said it would be making an extra fuel stop in Darwin for some of its flights between Australia and Bali in case it is forced to turn back.
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