The national disaster management agency said many people have fled because they are unsure of their proximity to a 12km exclusion zone imposed around the crater.
Mount Agung's eruption ni 1963 was one of the most powerful eruptions ever recorded and resulted in thousands killed.
"We've got like 20, 30, 40 shakes where you could feel the earth shaking", Lange, 30, told AFP.
The volcano's alert status was raised to its highest level on Friday, with hundreds of tremors daily indicating a high chance it will erupt.
The animals are extremely valuable to the evacuees - mostly farmers - some of whom have refused to leave the danger zone, the spokesman said.
Elsewhere in the Pacific, all 11,000 residents of the island of Ambae in Vanuatu were evacuated when the Manaro Voui volcano erupted last weekend.
The Manaro Voui volcano, which last erupted in 2005, sent up a plume of steam and ash over the weekend, prompting authorities to declare a state of emergency.
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"If my house is destroyed I don't know how to restart my life".
The mountain, about 70 kilometres to the northeast of the tourist hotspot of Kuta, is among more than 120 active volcanoes in Indonesia. Many of these show high levels of activity but it can be weeks or even months before an actual eruption.
"I am representing the Ministry of Transportation in expressing our deep concern and empathy to everyone being displaced from their homes due to the potential eruption of Mount Agung". Bali authorities urged holidaymakers to continue visiting the island.
On Wednesday, a New Zealand Defence Force (NZDF) aerial survey found "huge columns of smoke, ash and volcanic rocks billowing from the crater of an erupting volcano" on the island, according to a press release from the agency.
Several airlines in Singapore and Australia said they are preparing for disruptions, but that flights were running normally for now.
There is already a comprehensive plan in place to divert flights to 10 other airports across Indonesia, should ash and volcanic gases interrupt scheduled flight plans.